Father Passed Away Now Nursing Sending Lawyer For Payment Of Care

My father as been sick since 2007, he as been in and out of nursing homes and hospitals since. Now for the past two years he was in nursing homes which took care of him till his death. he only had Medicare from the state. He and my mother had a home together which was put in my name shortly after death. Now after almost 6 months the nursing is pursuing me for payment of care which is over 350k. Would I be liable for this or can they some how put a lien on my home ( which I live in and have always lived in) . Anyone ever been thru something like this? I’m in California