The son is a "holdover" in a "tenancy at will" -- in effect, a guest of his mother (who I presume is entitled to retain possession of the property during her lifetime). A tenancy at will may be terminated at any time, for any reason or for no reason at all. Consequently, when the mother passes, the trustee can serve notice of termination of tenancy on the son, and if he refuses to vacate the premises, then the trustee can sue to remove the son as a holdover from the tenancy at will.
Note: I am somewhat trivializing this procedure. Holdover tenancy actions can become difficult, because without a written lease, it's difficult for the court to ascertain the facts of the case. Ideally, if the trustee can get the mother and son to sign a lease, now -- even if the rental amount is $1.00 per month, that would make things much easier in the future.
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