Unless this is very specialized casual jargon word for the medical field, then this bad sentence with broken grammar or typos. Mobile autocorrect?
Recently I got passed off an older woman to admit
an older woman with crippling anxiety for geripsych placement.
I think the author used this: Dictionary: to pass sth. to so.
Because of "got", I expect the verb to be the in past tense. (passed)
The author received a patient for admission. They received the patient from somewhere/someone else.
I don't know why "off" is used, because then it could be Dictionary: to pass so./sth. off as sth. But this is now nonsensical. There's no "as" and no transformation object result. Nonsense.
If this is a casual jargon noun inside the medical field, then I expect an article (a/the). (Example: I got a passoff to admit an older woman).