If both parents need to go into nursing and are both on Medicaid, the house is in a trust, how is the house maintained financially?

You need to consult an elder law attorney.

I'd like to know the answe to that too

If your parents qualify, Medicaid may pay what your parents can't. You are not financially responsible for your parents cost care. Since Trusts are picky you will need to talk to the lawyer who set it up. Also, it would beca good idea to talk to an Elder lawyer about what needs to be done to place your parents.

What KIND of trust is the home in.
Because whether held in a trust or not, it will still be subject to medicaid recovery laws, whether held in trust or not, unless that trust is an IRREVOCABLE TRUST that already essentially gave away the home while the poor elders are expected to live out their lives in subminimal care in a Medicaid ECF.
In that case, perhaps the person who is the Trustee of that Trust can check to see if it is funded with cash to maintain the home in it. And in that case the person who is the beneficiary of everything and who will inherit the house without the taxpayer recovery of any money expended on the parents had BETTER keep up the house, right? Unless they want to inherit a worthless mess.

These things are basically legal questions about which you should check with an attorney who drew these things up. You can't afford to be wrong and we are just a bunch of caregivers who can tell you how to handle Aunt Edna's bad behavior at bingo. You can't be wrong about legal questions; that means you take them to an attorney.

I can't answer about the property tax discounts (the house would be still in their name in the trust, but if they don't actually reside in the home any longer...) If they don't provide any way to pay for the maintenance of the house within the trust (like some fund or investment that generates income), then you will need to pay for it -- and also the property taxes, insurance, professional fees (like paying for legal guidance regarding the trust, etc. Sounds like this isn't something that has yet happened. Trusts can be tricky and we aren't professions... just caregivers...so I strongly encourage your parents to invest in a consult with a certified elder law attorney or estate attorney so they get accurate advice.