My question involves estate proceedings in the state of: connecticut

My mother and father have recently moved into an assisted living facility, they are in their upper 80s. Their long term health care policies will cover the cost of assisted living for the next 6 years and, after that, they have significant assets in a retirement account, which generates some yearly income.
They also have a residence which is vacant now. The want to give me the house. I am the only heir.
I would need to put some money into renovating the house before I move in, but I am hesitant to do so since the house is not in my name.

I spoke to a lawyer he suggested that my parents should gift the house to me. The risk for them is that if they do gift the house they could not apply for medicaide for 5 years, but since they are covered by LT insurance for 6 years, and beyond that they have significant assets, it is a favorable situation. Also I don't plan to sell the house so no issue there. Are there any other possible pitfalls?
Looking for a second opinion from this group. Thanks!