by Federal Law. However, the Fed does allow debtors to file and elect their home state exemptions where they exist (property a person(s) is allowed to exempt from his/her creditors). But that would have no bearing on the question asked by motoconcho.
Credit card debt, mortgage debt, car loan debt, and other debt not associated with the "welfare" of the individual is not the obligation of the sponsor unless he/she is joint obligor on that account.
What you have here is an overlap of Federal Immigration Law and U.S. Bankruptcy law (what debt is dischargeable and who may or may not be responsible for that debt).
As you can probably guess, motoconcho's question is not a new one. In fact the circumstances he presents come up a great deal. And I too recommend motoconcho seek the advice of a competent Immigration Lawyer. At this juncture, it appears only his wife needs the counsel of a Bankruptcy practitioner.
Respectfully,
Playacaribe2