Spending down savings to qualify for medicare

My great aunt is getting very old and since she never married or had children, she has few people to care for her. My mother, her niece, does as much as she can, but we live many hours from her. She has broken her hip twice and is now in a nursing home but wants desperately to keep her little apartment and a sense of independence. She’s having to spend down her entire savings in order to qualify for Medicare so she can stay in the so-so facility she’s in now. It seems like it would be less expensive for her to live in her own place and have Medicare pay for a nurse to look in on her twice a day, since she doesn’t really need 24 hour care.