question about medicare/medicaid

So recently my dad has been sick on and off and so my mom wanted to the house part settled. Basically my dad is fully disabled, has no assets besides our house in which he has 200k equity in, and only income is ssdi. From what I know he has medicare/medicaid currently, the thing is my mom wants him to transfer the house to my name in order to be safe/secure if anything were to happen. So from talking to a lawyer though the only thing I am not sure of is the insurance part, they said he can transfer the deed fully to my name, it won’t affect the mortgage or home insurance, and that on my end it wouldn’t affect my college aid. They said they are not sure about how his medicaid/medicare coverage will get affected, and from research I am not sure either. He is already getting both medicaid/medicare with the asset under his name, and so I don’t see how transferring the deed would change anything. I saw for the long-term facility care thing theirs an issue with that perhaps, but my dad will never go to one, and so if thats the only thing is their anything else I am missing?