Before I begin answering your question, we have to make a few points in the situation clear.
I am clearing up these points, because maybe the problem could've been prevented in the first place, maybe some actions were taking too quickly without thinking through.

• When you get a new renter, you do some research. Do the renters have a good financial background? Was there still a husband to that mother when they moved in? Was it checked that the mother could keep paying rent if the 2 break up?
• How is the relationship between me and the mother? Is it like friendship, or just like a "customer" ?
  And if you DON'T know the person very well, how do you know that she's telling the truth, maybe she didn't even ask her family first? Maybe she would ask her landlord FIRST, who she doesn't know well, rather than having a very unpleasant conversation with her parents?
• She is responsible for the kids. If she can't afford the rent anymore, it's her responsibility to find a new apartment, in TIME, that she can't afford. because she risks losing her kids otherwise. If she can't pay rent at all, she can go to a social facility for women and children.

The mother has a very serious problem. But it's not her right to push that problem onto you. You are only the landlord, not her sponsor. You have nothing to do with her problems.

If you help her, your bank reputation score lowers, or you might lose the property, and make your own future worse.

It won't be great for her either, because she will feel even worse, knowing that she has badly influenced someone else's life.