I've not heard of any hospital taking a person's house to pay a medical bill. Typically it goes into collections and on your credit report. Now a lowered credit score will affect the ability to get loans, possibly needed to effect repairs on a home, but that is a bit more of a stretch. And if it goes to court then wages can be garnished, affecting your ability to pay a mortgage -- but I believe that garnished wages are limited.

Oh, and if you pay almost any amount on a monthly basis towards a medical bill, then that can keep it out of collections too.