Can the state take my home if I am the caregiver for a parent who will eventually need a higher level of care than I can give?

If the new home is titled solely in your name, then your father has made a gift to your of the equity from his former home, and if he applies for Medicaid within 5 years, that gift will cause a period of disqualification.

If the home is titled in joint names, then as long as the value of his joint interest in the new home at least equals his equity in the house he sold, no gift is made. Then, if your care for your father (for at least the two-year period immediately preceding his entering the nursing home) enabled him to delay going to the home, he can legally transfer his interest in the home at that time, and there will be no transfer penalty. If you plan to go this route, you will need (i) a letter from a physician indicating that your father is in need of nursing-home-level care, and (ii) detailed records of what you do to care for him. Your state may have additional requirements you should find out about. The state will want this should your father later sign a deed of his interest over to you (after he enters the nursing home), to avoid characterizing the deed as a gift.

I think this question has two parts: whose name will be on the title of the house, and which state is the house in?

In my state, if a relative lives in the parent's house AND makes it possible for the parent to avoid Medicaid-funded housing for two years, the house is exempt from Medicaid reclamation processing.

If the house will be titled in your name, I have no sure idea how the condo equity plays in, but there are generally rules against transferring assets to a relative to avoid Medicaid reclamation. If you run afoul of those, the state will absolutely force you to sell.

If the house is titled in your name, I don't think the state can force YOU to sell, but what they would probably do is disallowed Medicaid payment for your father in a facility for a certain number of months. BEFORE you do anything that you can't take back, you should see a NAELA certified eldercare attorney about asset protection. Gabriel Hauser, an attorney who posts on this forum, has written a book on this topic, if you feel you have time to review it.