I'm sorry to hear of these difficulties especially after dealing with your family loss.
When there is an executor an an estate, that person has a fidcuiary obligation to the estate to ensure that the property is being rented out at fair market value. If the current arrangement is not fair market value, and there is no lease, then the executor must follow legal protocol to remove the person from the home.
If the executor does not do this and the person remains in the home for below fair market value (FMV) then the executor is liable for the difference.
The executor may not arbitrarily assign a retroactive rental amount.
If the heirs choose to sell the home, then the proceeds are divided according to the terms of the will/trust.
So basically if a person lives in a residence without a written agreement, the courts will enforce the "oral agreement". if there is no oral agreement, then the courts will generally allow the person to live in the home until eviction occurs (because long term "tenants" even without a lease, have rights). If the person has already moved out, it will be difficult for the executor to establish rent if rent was never paid.
If there is in fact a rental agreement, as executor, the executor must attempt to recoup the rent. But if the person was allowed to live there rent free, there is not much legal recourse.