I wouldn’t worry about having to move in a month. Look at it from your landlord’s point of view. She wants you to stay there and pay her each month.
She’s probably pretty desperate at this point if she is asking you if you are interested because now she risks losing you as a renter. If she goes into foreclosure you’ll be able to stay there until it all gets sorted out and then a bank may want to keep you as a renter, or maybe not, but it’ll take months for everything to happen.
Is it the ideal situation, no, but if your main worry is staying for a few more months, I wouldn’t worry.