A pass (for schools, military, etc.) exempting one from regular activities, to instead visit a hospital for treatment
A poorly executed pass to a team-mate, who is likely to lose the ball as a result. (Originally rugby union, where the recipient of a hospital pass is a sitting duck for a hard tackle.)
(by extension) a promotion or delegation which is likely to end in failure or ignominy; a poisoned chalice
(Ultimate Frisbee) A throw that stays in the air long enough that it allows too many people to get underneath it, increasing the risk of injury and a trip to the hospital.