If someone is too delusional to place in a home or hard to place, then what happens to them?

Question

Do they stay in the hospital forever until a place says "Yes"? Or are they just eventually released into society? How common is this?

Answer 1

It's not entirely uncommon, though I don't have any idea of the actual frequency of hospital placement.

But yes, you are correct.  If they cannot be placed in a low-security environment such as an assisted living facility, then they are placed in a higher-security mental hospital.