I agree with Jeff.  If the taxpayer did not benefit from the home until the parent died, it seems likely it is a Life Estate.  If it is a Life Estate, it gets the step-up in Basis at the date of death of the parents.

A $1 transaction fee for a home is not really a sale, it is just part of transferring the title.  If the taxpayer had used the home after that transfer, it probably would have been a Gift, in which case the Basis would be the Basis of the parent.  But as I mentioned above, it seems likely it is a Life Estate.