Oh yeah. This assumption and idk if in korea banks operate the same way. But usually if one has a debt wuth late paryment history under their name + low income in mind, it is less likely that the bank will loan them more if they think the person can't pay it. So my theory is that the ex already asked the bank for money to buy their basement house which is under his name if I'm not wrong. Thus when he needed money to pay for her medical bills they both agree to put in other her name. Which explain a bit why she doesn't hate him for getting both of them in debt.

Question is this debt she and her ex accumulated together?