Is my motherin law obligaed to pay the charges for my deceased father in law's auto lease?

My father in law leased a car in Florida in November of 2013. He died in May of 2014. My mother in law isn't listed as a co-lessee nr had she signed anything relative to the transaction. After his death my sister in law called the dealership and was told the lease could be ended early if the car was returned along with a death certificate, which was promptly done. My mother in law recently received a letter addressed to my deceased father in law that state that he owes over $4K for ending the lease early. My question; since my mother in law is not named in the lease nor had she signed any paperwork, is she responsible for the charges?