When we were contemplating long term care for a family member, the nursing homes made it abundantly clear that Medicaid did not mean "free" care. It meant Medicaid would go after every dollar in assets from the patient both while alive and after death.
When my mother was in a nursing home, my brother applied for Medicaid. Mom passed on before the application was process was completed. But it surprised me when my bro told me Medicaid here in PA did not demand the house. Now, this was a few years ago; perhaps the law has changed. But that's the way it was back then.