Fraudulent transfer to avoid debt

This is in California. My father just passed away. I have power of attorney for him. About 6 months prior to his passing, his home was put into my name as well as "non-resident co-owner." He had to be put on Medi-Cal as he was going to have to permanently stay in a sub-acute facility. The house was "exempted" by Medi-Cal and I took on part ownership since that was the only way that I could sell it. The house sold in December and is in escrow. When dad died in January, I assumed full ownership. All of dad's assets were a life insurance policy and the house and under $100,000. I understand that creditors cannot come after joint tenancy property and life insurance that has a designated beneficiary (which it does). However, I was also told that "if my name was added shortly before death, it *may* be able to be attacked as a fraudulent transfer intended to avoid creditors." What is considered "shortly before death" and do the factors of how and why I took on ownership affect this?