Can a home be put into trust?

If they went in on Medicaid, it is already too late to do this. These things have to be done at least 5 years before you apply to Medicaid.
The disabled grandchild would not qualify. It has to be a disabled son or daughter already living in the home as a primary residence

As an aside on this, putting a house in a trust so that the ownership of the property reads in all paperwork & property /assessors records as "XYZ trust" will pose other issues in addition to what Pam mentioned. The traditional homeowners insurance (state farm, Allstate types) usually will NOT do homeowners insurance for a trust. So you will need to get a speciality carrier which will cost more and perhaps have less coverage. Also should you need to ever look into getting a HELOC or other equity use on the property, being in a trust makes doing this really really hard. Banks, mortgage companies, lenders etc are set up to either do biz with individuals or business entites (like INCs, LLCs) and usually not with a trust. An individual trust that is a single property means no recourse for a lender so they will pass on doing any business as too much risk. If you do a trust IMHO it needs to be such that the house is just one of many items owned by & in the trust so that there is real value, real assets that produce income to fund the trust.

How is the NH being paid?
Will they need to eventually apply for Medicaid?
Who is the named heir in their will?

If medicaid will be needed, their home is subject to MERP, which is attempt by the state to recover costs spent on their care by medicaid. MERP has all sorts of exemptions, exclusions & requires a cost benefit analysis to be done. If the heir is disabled (this will need to be verifiable), that will likely be an exemption to MERP. So is grandchild the heir in their will? If not, are they competent & cognitive enough to do a codicil to the will naming grandchild?

. If the property is low value and family has documentation for paying for maintenance and the required on the empty property (taxes, insurance, etc), the recovery could be below the Cost -benefit amount to do a MERP recovery. If you go this route, you must MUST keep meticulous records on every penny spent on the property. And you will have to do this from day 1 of Medicaid till they die and then (probably) through the probate process ( which will have it's own costs). It's a long term commitment to keep the home.

Keeping your parents home will require you to front all cost$$'s as medicaid will require of them to pay their monthly income (their SS & retirement) to the NH each month as the required by medicaid co-pay. Roof needs repair, its on you to pay. To me, it's like having a 2nd home but with no ownership so runs risk. Most families cannot afford a 2nd home and are risk adverse, so the house gets sold with the proceeds of the sale going towards private pay at a facility. Some rent the parents home and deal with that paperwork with medicaid. IF the house is really low value, it will cover just a couple of months at best as NH run 5K- 15k and you have not 1 but both parents in a NH. The costs are staggering.

I'd suggest you put pen to paper to see what the "nut" on parents home is and whether you can afford it all totally on your own for possibly several years. Family doing this as a shared cost seems to end up with folks all nice & cooperative for a few months and then won't do or pay whatever over time. Good luck.