For clarification, is the "home owner" the same as the "staying in the nursing" home or the current "tenant" of the home?
First: If the trust has given the "home owner" the right to live in the home for the rest of the "home owner's" life, yet the "home owner" and the trust can come to a written agreement removing this right, i.e. doctors orders that the "home owner" must remain in the nursing home due to ill heath or because the Trust deems it necessary, this right can be removed.
Second: If the "home owner" and the individual/persons currently renting the home are not the same person and the trust and the "home owner" come to a written agreement removing the right to occupy the property for the remainder of the "home owner's" life, the Trust can not renew/extend the current individual/person's lease on the property's and sale the property vacant or sale the property to an investor while still rented and the purchaser can raise the rent rates to market value once the lease is up for renewal/extension.
Third: If you do sale out of both homes, you will have enough cash on hand to place a large enough down payment w/ any rent-to-own options in Oregon, check the local papers for these options.
Every problem has more than one solutions, these are just some thoughts.