Nope, if they don't pay, it's YOUR problem, not theirs, and you wouldn't be allowed to continue.
If you're concerned about debt - and it's a very legitimate concern! - then one option might be to pass on college for a year, get a job, and apply to a different set of colleges for the following year where you'd qualify for enough merit aid to pay your expenses.
But, with debt of only $5000/year, you might be able to get a summer job that would cover a good chunk of this . . . in which case you can repay the loans immediately and graduate with significantly less debt.
Honestly, it's unlikely you'll find a school that would give you a better deal than you already have.