Can your sister continue to reside in a home that was bought for her by our deceased father if he willed it to her and he was the only mortgage holder?

Provided the estate is solvent, she should be able to obtain the title to the home, subject to the remaining mortgage. She can remain in the home, but will have to satisfy the finance company's lien on the home through a new mortgage or paying it off. There may be additional clauses in the will directing that the mortgage be paid off by the estate. The executor of the estate, or their legal counsel, will be able to answer these questions.