Mentally ill senior citizen in independent housing getting a notice to comply or else. Is this right?

She does need to comply with the rules of the place she lives. If she can't, then it isn't the right place for her. It may be that she needs to be in a place that provides more services for her, such as assisted living or a group home. She is mentally ill and does not have much money apparently, so a good place to start would be the county's Adult Protection services with the Human Resources Dept. They should be able to evaluate her needs and find a suitable place for her to live. She does not need to be on the street, but she may need to live somewhere else. There is no right or wrong in what is happening. It may just need a bit of county intervention, given her problems.

What exactly is the issue with the refrigerator? Is it a matter of cleaning it?

My mother was in subsidized housing and had regular inspections of her apartment. The place had to be generally clean and the fridge sanitary with no outdated food. (I think this was twice a year.) Her family helped do a thorough cleaning before these inspections (and a few other times as well). As Mom's health declined we called Social Services for a needs evaluation. Mom got homekeeping services -- laundry and cleaning -- as well as a visiting nurse. This allowed her to remain in her apartment for a few more years. She is now in a nursing home.

I think that you are going to find that this person is eligible for more assistance, either where she is or in another level of care. You are very kind to care. I hope you will be able to get the ball rolling to get more care for her. Since she is on SSDI, she probably has a case worker. If you can find out who that is that might be a good place to start.