Others have shared some good resources like adult protective services---definitely check them out. Others have also pointed out that long term adult care is very expensive. All I have to add is that I do know of someone who was in a similar situation as you. She likewise no longer lived in the city and her mother became too invalid to live alone.

As her mother was their last link to the city (no other family in the area who would be coming in to visit her or help the family out in case of an emergency), they found an assisted living facility in the Midwest that was very nice and much cheaper than in the NYC area.

For them it just made sense. Once in any facility it did not matter much to her mother, only that it was to a standard that they wanted for her care and happiness. For them, it was much cheaper and they made sure to choose somewhere that they could get in and out of easily (close to a major Midwestern airport). They found that they could either spend the same amount as NYC was going to cost, but get a much nicer facility and level of care/attention OR go with the basic standard that they were going to get in NYC and use the money saved for my friend to make more visits to see her mother.

In the end, they found something in between those two choices and have been very happy with the result. Her facility is in a moderately small town that has that Midwestern work / cleanliness / accountability ethic, so they always feel like the staff wants her/them to be pleased and on-board with what is going on.

Just something to consider, so you know that there are many options. If you are already 5,000 miles away does it matter if she is in the city or maybe there's a great place elsewhere that has much cheaper eldercare...