This is a variation of the bad gift circuit, where the bad gift goes back and forth. That usually happens with two people, usually brothers who give back and forth the same hankerchief every year at Christmas. Bad gifts are not as likely to pass through a larger amount of people. Someone will keep the gift. But an impossible gift keeps moving.
Variation: "Impossible Gift Club" there is an undefined comaraderie among the people who have once owned the gift. They all privately think it is funny. But it is in in such poor taste that it is the humor that dare not speak its name.
Once the impossible gift has gone one full circuit, the original gifter gives it again to his first recipient, and the circuit continues with each receipient knowing they are part of a group of people who appreciate truly bad taste.
Don't Turn a Rape Into a Murder
Some people will privately think that's funny, but they can't wear it publicly. No way.
So if Johnny gives it to Hank. Hank will say "Wow. That's sick. Some T shirts try to be sick, saying things like 'I got drunk on Spring Break and won a wet T shirt contest' but this is really sick. I wish could wear it, but I'll get in trouble. It's impossible to use. So it will just sit in my drawer."
Johnny says: "You can give it someone else as a present."
So the T shirt is gifted and regifted but never worn. Eventually someone gifts the shirt to Johnny, the original gifter. It has gone full impossible gift circuit. It will happen.
And so they have defined the "Impossible Gift Club"