SJSinNYC:
She has Bitachon that she will be able to pay (she is not planning on not paying). That is enough for a yeshiva/sale. For a loan, you would be required to have means to pay back (I think).
Besides, she probably has assets that can be used to collect, if the school/creditors really needed to (C”V) do so.
And even if not, the school should still accept her children.