I've been a professional loan collector for years now. (There's a difference between a lender and collector - the problem is your "Aunt" met lenders who were NOT collectors - too much of that happened in the USA)
My experience has taught me many things, allow me to share a few:
1) Never make a loan without a clear and visible repayment/takeout/exit strategy - this "loan" fails that test, as did the original mortgage on her house!
2) Never make a Loan (in your mind) that you know you doesn't meet the criteria of #1 - a gift is another story
3) Sometimes the best way to help is to allow someone to hit bottom and then be there for them - it seems that this is the case here - lend her money after she has declared bankruptcy - which she should do right away - that way she can start fresh and your cash will be last months rent plus security deposit on something she can afford
We have an expression for where you're at - we call it "Financing a Black Hole" - there is no amount of cash you can give her to fix her problem - she's venting oxygen into space! THe math you've done doesn't include taxes, income, property, etc. as well as incidentals - using the 30% rule, she should spend no more than 30% of her gross income on Housing payments.
The issue with US lending practices lately has been that all the traditional rules of thumb were thrown out the window to everyone's detriment, the borrower shouldn't have been able to get a loan that they couldn't pay, the lender shouldn't have made a loan they couldn't collect on and the securitization should not have been accepted by anyone since the two basic parties didn't comply with logical norms.
I've seen the actual documents and all I can say is that they were written with a "Bullshit Baffles Brains" approach to ensure that nobody would read and understand what they were really buying - FRAUD in my mind!