My day job's a mortgage underwriter and I'm doing a course for being a financial advisor (although I'm not half way through it yet), so I'm not an expert but I know a bit about property law. Warning: UK, not USA. But the main principles will be similar enough. Get someone from the USA to check all the details.
Who owns the house? If his parents owned the house mortgage free, and left it to him in their will, it's his. No-one can repossess it. If they didn't leave a will, he'd inherit it anyway as he's their surviving next of kin (check intestate law in the appropriate state though - these things tend to vary by jurisdiction).
The bank would repossess a home only if there is a mortgage on it that's not being paid. There is no other reason why a bank would have any claim on the house. (In the USA I hear the term "home loan" a lot - not sure if this is technically a mortgage or some other kind of loan, but either way, the is no loan on the house = no repossession.)
For example, if he inherited the house with a mortgage but his parents had no life insurance (normally life insurance pays out enough to pay off the mortgage so the kids would inherit it mortgage free), then he'd inherit the mortgage as well. In theory this could lead to the house getting repossessed if he didn't make payments, however usually when someone inherits a property with a mortgage on it, the probate solicitors will sell the house, pay the bank what's owed on the mortgage, and the surviving relatives inherit what's left (per the will, or per the law for how to share out someone's estate where there's no will). So I wouldn't find it plausible that he'd inherit a house which is then repossessed by the bank, UNLESS he remortgaged it himself after inheriting it and then failed to make the mortgage payments. This wouldn't happen within a 1 year timescale though. Probate itself takes more than a year (solicitors are bloody slow).
Solicitor = UK lawyer that deals with boring stuff like property, wills etc. The other kind of lawyer is a barrister, who does more flashy stuff like criminal law.
If you want him to inherit the house and for it to be abandoned for a year after he inherits it, you'd need for it to be inherited mortgage free, either because his parents paid off all the mortgage before dying (or were rich enough to purchase it outright) or because they had a life insurance policy that paid the mortgage. However IMO you'd need an in story reason for why he didn't either live in the house, rent it out, remortgage it or sell it and instead chose to be in debt (he needs a financial advisor lol). He could've remortgaged it to pay the hospital bills then rented it out so the rental income covered the mortgage repayments and gave him a bit extra as well.
On the other hand, if you want him to be in big debt/financial trouble for a year before he gets his hands on the house then the most obvious explanation to me would be that the solicitors took their time sorting out all the probate - a year is actually quite quick for probate solicitors, so you can drag it out longer than that if you want. So he couldn't do anything about the hospital debt in all that time. Useless solicitors = he eventually gets the house he's inherited and it's in a crap state because no-one looked after it. Sounds like he didn't have enough money to pay for someone to keep it nice. Note: obviously it may be different in the USA, if you have super fast lawyers that deal with this stuff then I'd be pleasantly surprised.
Also note: in the UK you can rent out an inherited property before you technically own it. I know because I've assessed mortgage applications like this - property is still in the deceased person's name but it's already being rented out by the person who inherited it. The situation isn't even that rare, to be honest. I don't know how this would pan out in USA law though - it's probably different in different states so you'd have to find out for the specific state your story's set in. It's something to consider though, because if he can "own" it and live in it or rent it out before the solicitors officially transfer ownership of the house to him, then you have to consider how that fits in with him being in financial dire straits for a year.