My players decided to try summoning an elder god in order to gain immortality in Call of Cthulhu. Your best ideas for how this will inevitably go horribly wrong?

This particular 'elder god' is more of a mantle, you see. This entity does wield great powers, but is also beholden to a horrible and cursed collection of duties. During the summoning, they accidentally, somehow, kill this elder god; due to the nature of the summoning they must now assume his mantle and fulfill his obligations, with all that entails, lest the cosmos fall. A Satan Clause, if you will.

My go-to is to always grant immortality and nothing else. "Okay, you can no longer die." Do they age? Yes. Get sick? Yes. Experience pain? Dismemberment? Senility, malnutrition, atrophy, and dessication? Absolutely. They can do everything they could do previously, except die.

The bad news: Summoning an entire elder god is hard. They end up summoning one of the innumerable lesser horrors in the elder god's orbit.

The good news: The summoned entity is going to grant them immortality.

The bad news: The players will experience an eternity of never-ending horror and torment.

The good news: Since it's just a (relatively) lesser entity, the players actually have a slim chance of ending this curse, returning to blissful mortality.

The go-to monkey paw scenario could work, where they receive immortality, but have to serve the summoned entity forever as deformed (and perhaps always hurting) "things"? However, that is maybe a bit too predictable. What if they mess up the spell and instead mark themselves for sacrifice?

They slowly realise this due to a symbol appearing on them, which could slowly spread further on their body (maybe hurting too). You could make it more interesting by pitting them against one another by suggesting that only a few have to die for the sacrifice to be complete. If their characters are not that close to one another, it could lead to some interesting decisions on their part, haha.

The process could span a week or more, where their body gets engulfed more and more by the mark. They could use this time to review what went wrong in the summoning process, and how to potentially reverse it. I'll leave those details to you, if you're interested in pursuing this idea :D

This is the kind of ritual that usually ends with 4 missing and 1 insane. Have they ever thought that they might visit Kadath?

I mean come on, how many times do you have to have to hear "there are worse fates than death" in cosmic horror? You know exactly what to do.

Which God?

My first reaction would be that they summon, permit it to enter our world, and are the first ones to die as the entity/god just doesn't care.

Inspiration could be found in End of the world: wrath of the gods, or Fate of Cthulhu.

Or the original followers become their ennemies to be the first to summon the gods.

Congratulations! Your players have become the villains of the campaign. What should you expect when this happens?

Well, summoning an elder god is an extremely stupid foolish idiot thing to do. An Elder God cannot be reasoned with or controlled by a pathetic mortal and attempting to get its attention will likely get a dozen square miles flattened like God swatting a flea.

But if you’re arrogant or greedy or shortsighted enough to want to do it anyways, then you’ve got a lot of work to do. At the very least, you’re going to need a complete copy of the necronomicon, which will be near-impossible to find and definitely impossible to retrieve without committing some heinous crimes. Plus you’ll need some ritual artifacts from cyclopean remnants deep beneath the sea or under the ice in the antarctic. And to get all those, you need money, power, and connections so I hope you like dealing with the Mob. Plus your body will need to be altered to survive channeling that much arcane power, so I hope you like mutating into something that makes Wilbur Whately look like Adonis.

And naturally while you’re doing all this, a group of random shmoes will stumble onto your conspiracy and band together as a group of Investigators to try and stop you beginning an apocalypse. There’ll be some back and forth as you send minions to deal with them, trap them, race them, etc., but they almost certainly will be there right as you are culminating your great summoning ritual. Then it’s all up to the dice: either you win, summon an Elder God, and get everything in the zip code including yourself killed for annoying it; or you lose, and an investigator puts a .44 through your soft cartilaginous skull.

Have them roll a perception check just prior to the ritual.

Surprise, they're the villains and a party of heroes shows up to fight them. If they don't spot the ambushing party of heroes, they'll be hit by some serious AoE spell and an assassination attempt on one of them a turn or so later.

If they win the fight and successfully summon the elder god, they have to start rolling wisdom saves or something to resist mind control, and the ones that fail and have to roll every 1-3 turns or something to try to get control again. All the while they become surrounded by not just the massive elder god but a swarm of enemies that won't hesitate to attack any party member that disobeys the elder god's orders. It'll be up to the other players whether to enter combat to try to defend their friend against the hopelessly large assault.

But what does the elder god tell them to do? Go backwards and ravage every single place the players have visited during the campaign, and maybe some random villages along the way if you need filler.

Maybe you start impromptu adding a d4 or d6 psychic damage to their attack rolls as an unconventional way to empower them. Maybe play favorites, maybe add 2d6 to the weakest member's main attack to boost them and their ego.

If it goes far and long enough maybe you start having them war against empire, do something unconventional and treat legions as single units with one health pool and doing an arrow barrage or a 'charge' that does some damage and then becomes more of a sustained melee that essentially becomes a DoT effect as far as the combat system is concerned. Like an insect swarm.

Should they successfully destroy the army and seize the seat of power, find some messed up way to do a "game over", or come here and ask again. These players want to see the game go in dramatic and strange directions.

I don't play DnD so I guess a lot of this might not be doable/practical.

Also after reading some other responses, particularly the one about how this kind of ritual is usually portrayed as requiring a bit more than a few friends, some magic words and a wish, it may or may not work better if you have a bit of backlash, scarring, and some aberrations respond to the attempt, instead of the elder god. Maybe have them run around a town or two recruiting cultists for a second attempt, something like 15-30 of them. There could also be some drama where the cultists question who is the authority as a few other cultists move to take the lead.

Give them what they want, against an eternity of slavery and suffering. Looks like a nice final episode for a campaign

Some ideas I'd love to do to my players if I still played games like this (I'm old):

Parasitic Immortality: Each player’s body now harbors a sentient, parasitic entity from the elder god's realm. To stay alive, the player must feed the parasite by draining the life of others, and the parasite is very specific of who to consume and when. If they fail, the parasite consumes them from the inside, painfully regenerating them each time but with diminishing humanity.

Memory Reset: The players are indeed immortal, but each time they sleep, they lose a random set of memories or skills. Over centuries, they become strangers to themselves, unsure of their origins, skills, or even motivations. (Think Momento)

Unwanted Guests: Each player's soul is bound to their body forever, but their mind becomes vulnerable to invasion by the elder god's minions. Between play sessions, they find themselves "sharing" their consciousness with malevolent spirits who take control at unpredictable times and start the next play session in terrible or awkward scenarios. (Think GTA V when you switch characters, but more fucked up)

Mosaic Body: Their bodies no longer age, but they start falling apart, requiring constant replacement. They can survive only by patching themselves up with body parts from other beings, creating a grotesque patchwork appearance, and everything hurts. The more messed up ways to gain body parts the better. (Frankenstein's Monster)

Eternal Decay: The god grants them eternal life, but not eternal youth. They’re doomed to experience endless decay, enduring the sensation and accelerated loss of flesh, muscle, and sensation as their bodies remain animated corpses over months instead of decades.

Mirror Life: Between play sessions they wake up in a universe where their actions had the opposite outcome. Friends become enemies, achievements become failures, and they are eternally tormented by a reality where their efforts always yield the worst.

Bound to Territory: They live forever, but their bodies are tethered to a specific region—a cursed ground created by the elder god. If they stray too far, they wither, eventually getting pulled back in by an unseen force to endure perpetual cycles of death and rebirth.

Soul Fracture: Their souls split into multiple pieces, scattered across different planes. They’re immortal, but constantly feel the pain and emotions of all their fractured selves, and each piece they “reclaim” in other worlds is hostile, violent, and deranged.

He Lied: The elder god couldn't be trusted, he did some magic feeling and looking stuff that did nothing just to get these mortals to go away

Well it could eat them, but that's boring. Instead you could start giving them attributes that seem positive at first, but then start to turn negative, until eventually they start to realize that they're just being turned into shogoths.

There are different kinds of immortality.

They could be immortal like Deadpool. I don't think that's the most interesting option in a cosmic horror setting.

But why would the elder god grant the gift of healing? Why would he prevent the ravages of time? A thousand years from now, the immortal investigator will be no more than a surviving consciousness in a dried-up eye, enshrined in a relic, gazing out at the world for all eternity.

Or what if immortality was just the knowledge of a way to combat the ravages of time, but not violent death? What would be the price to pay? Absorbing the vital energy of other humans (or rarer, more dangerous entities) at regular intervals? Transfering their consciousness from other bodies ?

What would the investigators do to protect themselves physically and organize their survival? They'd need the means, the wealth, and reliable people at their service. How could they ensure their loyalty? How be sure they won't betray them to acquire their position or their secrets of eternel life?

At what point will they attract the attention of other dark cults or people acting to save humanity, like investigators or government agencies like Delta Green?

At some point, you could even start a new campaign in which their immortal characters are the hidden leaders of a dark cult that threatens the survival of mankind

I would let the total succeed in one or two of them only, they become intangible statues, living their life slowly enough that it will last until the end of the universe. The others end up drained of their life force and or go insane.