SLPT: Before taking what you think is the biggest shit of your life in the restroom of someone you barely know, make yourself a favor and flush the toilet once to make sure it is functional.
It's a good tip, but shitty.
This just happened to me in the guest bathroom of someone I barely knew. The bathroom was meters away from the meeting.
If the tank isn't filling for whatever reason just take off the lid and fill it with a water glass from the sink, or whatever is on hand. Once it's filled it will flush. Unless it's just totally blocked down below.