If there is no one where she's living now who will take care of her, I urge you to move her to your city; not to your home but to an assisted living home or perhaps a foster home. Gamma G. gave you some good information but it's my impression that she can no longer live with her daughter/daughter-in-law. So she needs a new home. Is that right?
You cannot take care of her long distance. She needs someone to check on her, talk with caretakers, see that her needs are met. You just cannot do that unless you live nearby. And I doubt that she can live alone in her own apartment and rely on outside help. Someone needs to co-ordinate that. She can get people to come in to help her if she's living with someone else. When did you see her, in person, last. I suggest that you need to know what her needs are and will only be able to know by personal experience.
I've helped to take care of both parents, my mother-in-law and am now helping a friend with serious health issues.
I've never heard of contacting the Public Housing Authority. Don't they help low income find housing? Sounds like your mother is not able to live on her own. I suggest PHA will not be able to help her.
I suggest you start by finding out what services are available in your community and find her an assisted living place. Google assisted living to find places, visit and talk about how to get her help. They will have a social worker on staff and be able to help you learn about how to get assistance, financial and otherwise.
Your community will also have an office that assists seniors. Again, you can find it by googling this. You can also talk with the state public assistance office to learn how to obtain financial assistance for her. They may not be willing to help someone not a residence so just give her address as yours even tho she isn't living with you at the moment.
There is help available. It just takes time and perseverance to find it. Start by calling one place and go from their. Gradually you'll find other numbers and other places to start. Google assistance for seniors and your community to get started.
Sounds like she does still have family ties in NM. Perhaps it would be better for someone there to take over by finding her a place to live and arranging for care and financial assistance.