well, not to be that guy but
she would be a princess in name only since her country is gone. and due to her now not holding an official position just an 'air title' she has no real authority.
as for the debt, if it was nation debt, that is gone with the country along with the ability to pay it off. so without playing the game i have to assume that it was a personal debt or something inherited from the family.
and even countries in extreme debt still exist as a country so long as they have political/ military/ and judicial power. as this is what they typically leverage to pay such debts, or atleast make payments.
Well, yes and no. It really depends on the setting.
Even if her country is gone, if there's a way to collect on a debt, the lender will sure as fuck try. Like the other guy said, generational debt is a thing. Though her title holds no power, she's still afforded privileges based on her pedigree alone. A wealthy man with no title may still want to wed her if the pedigree would help him or their heir get into social spheres unavailable to even wealthy commoners. She would also be a desirable candidate for any noble families that want to take the throne, as she is a recognized individual of royal descent. Failing that, whether by willing prostitution or slavery, she would still be worth more money than a common woman. If there's any money to be recovered, her lenders will be sure to try to collect. They'd only not do it if there wasn't worth it. Since she's only a princess in title and a refugee, she doesn't have any legal system of protection, even if the lender is in the wrong. She's not going to be recognized as a citizen and she doesn't have the political or military might to tell them to fuck off.