Home Ownership

A home is which an individual resides does not affect eligibility for SSI or Medicaid. This includes a home owned by a trust established for the person's benefit. 

Home Ownership. SI 01130.100 provides that an individual's home, defined as property in which he or she has an ownership interest and that serves as his or her principal place of residence, regardless of value, is an excluded resource. This means that the value of the house it does not affect SSI eligibility. 

SI 01110.515C provides that a beneficiary in a trust may not have legal title to the assets of the trust, but does have "an equitable ownership interest" in the trust.

 As set out here: Trust Expenditures and Public Entitlements

A person receiving SSI living in a house owned by some third party rent free IS affected. 
A person whose mortgage is being paid by a trust IS affected.
These things affect SSI only, not Medicaid and not Social Security Disability or Social Security Retirement
see: Confusing Nomenclature of Public Entitlements