Where to get aid for Mom to qualify getting in a place that's $3300 a month?

Mom with dementia at 101 yrs old must have care. Southern Calif dementia care is usually $7-10,000 a month and I have found a great place for only $3300 a month all inclusive but her total income is only $2300 a month. She does not need skilled nursing just help with all daily tasks and incontinence care. I am only relative and elderly myself and cannot lift or care for her. She is happy living where she is and they are not a Medicare facility. In fact I cannot find any facilities that accept Medicare for payment in southern CA. Is there any place to go to get aid?