Will he have to sell the house?

No, not if he pays a fair market price and the money is put in her account for her own care and only for her care.

If the house is sold at less than fair market value, that would be considered a gift and would have an impact on her eligibility for Medicaid if she needs to apply in the next 5 years.

But if a grandson or any body else buys the house at fair market value, then no gifting is involved.

Quit claim deeds are the devil. Like Pam said, you don't want to do a sale that way.

If he buys it, needs to be FMV based on legit appraisal if its for less than the tax assessor current value & via a Warranty Deed & with title insurance imho. It protects your son in this whole process as well.

Keep in mind that if she applies for Medicaid, the state can easily check to see what real property she owned - tied into by either her or her spouses (even if dead) name & or SS # - in the past decade plus as all the local tax assessor records are dovetailed into the state system. Any transfer of property will show up and to the penny.

If your Mum is able to pay for her own elderly care for the rest of her life, there wouldn't be an issue. If the State or Country needs to chip in, you will need to check the laws/rules.

Chrismey, let me give you an example. Grandma sells her home to grandson on a quit claim deed for $1. All seems well and good. Grandma goes in a nursing home on Medicaid and dies. Medicaid then files a claim against the house for $100,000 worth of NH bills. WHAT?
Grandson did not know that a "quit claim" only quits Grandma's claim to the property. He did not know there were NH bills, credit cards and a reverse mortgage on the house and those claims are all active and enforceable.
Grandson loses the house because he cannot pay off those debts.
Happens more often than you might think.