You do not directly guaranty or become obligated on the debt. But:1) Because you are obligated to support the person you are sponsoring, if his/her debt renders him involvent, you can be sued by him or her for support.2) You can be held liable to repay any public support or benefits (including medical benefits) the person you are sponsoring receives from the government--the government may sue to collect this. So an impoverished or debt ridden immigrant who receives benefits can then force you to repay those benefits.Therefore, while you do not directly guaranty specific debts (unless you fact choose to do so), you are so entangled with the person's finances that his/her debts can easily, albeit indirectly, rebound against you.