Linux has at least four levels of decreasing pleasantry: -1, -2, -15, and -9, aka HangUP, INTerrupt, TERMinate and KILL or "Please stop", "Hey! Quit it!", "Stop it! NOW!" and *loud gunshot*.
Sometimes processes will clean up after themselves and leave when asked nicely. Or sternly told off. Of course, if you don't need or want that, load up your, uh, -9 shooter.
You can try asking a process to round up its dead children, but unlike the quit signals, the number varies by platform. For most Linux users it's -17, but using the text version -CHLD is probably a better choice (unless you're on a really old system that absolutely has to have a number, in which case check the local documentation.)
If it's a well-behaved process, that can do away with the need to kill it. In other cases, there might be some kind of restart mechanism built in that can be called instead - assuming sending it a SIGCHLD doesn't trigger that behaviour anyway.
Case in point, the Cinnamon DE has at least a couple of ways to restart it, and at least one of those gets rid of its zombie child processes. It's fairly rare that I need to do that, and I haven't tried sending it a -17. I might do at some point.
I think I've seen a couple of their videos, and have no idea which of them Adam would be (can't even call any faces to mind right now to be fair), so I'm pretty sure those phrases are in my head from elsewhere.
The "Please stop" is pretty generic, but got a lot of traction that time Hyperbole and a Half told a story involving it. "Hey! Quit it!" is probably Lisa or Bart from some episode of The Simpsons. "Stop it! NOW!" is probably something that was actually said to me at some point as a kid.
Never got shot though, so I must have started behaving at that point.
(For legal reasons, that last part is meant to be tongue-in-cheek. I am also using "for legal reasons" mostly humorously. Mostly.)