The only "trust" that Medicaid will allow is a "Miller Trust". It goes by a different name in some states. When there is an overage the money is put in the Trust. When the person passes the Trust reverts back to Medicaid.
The house doesn't count as an asset. But also, Dad is not going to be able to keep it up. All his income will go to offset the cost of his care. You may have to sell it to pay off the Mortgage and what is left over will go for Dads care.
You may want to have an attorney do it for him. Another hurdle sometimes is the income if it is over a certain limit. His retirement and SS combined may be over the state's limit for LTC Medicaid, but it may be able to be structured with trusts to meet the state's requirements. As far as the house, normally Medicaid allows a home but may place a lien on it.
No it won’t help his Medicaid eligibility. He’s allowed to have a house while on Medicaid. Letting the house go in to foreclosure won’t make him eligible for Medicaid. Once he gets on Medicaid a nursing home, he will lose the house anyway because there won’t be money to pay the mortgage. See if your state allowes Miller trust’s/qualified income trusts, if that’s an option then his excess income will go to a trust account that Medicaid is beneficiary of and the money will go to them.
The house doesn't count as an asset. But also, Dad is not going to be able to keep it up. All his income will go to offset the cost of his care. You may have to sell it to pay off the Mortgage and what is left over will go for Dads care.