My dad is currently in the nursing home and they are trying to get him on medicaid. He only has his house as an asset valued @ $75K. will they take it

I'm his daughter, we are in TN. I'm sure they will take it but I've heard that a nursing home could come after me when he dies for any money owed that the house didn't cover. Not sure what or if there's something I need to do. He's only been there for 2 weeks but he needs to be transitioned to long term care which is $7000 a month. If he lives a long time that's a lot they could come after me for.