No, you probably would not be notified. In the first place, unless the lender was aware of the fraud or identity theft--i.e. the lender knew something was wrong--he/she/it would have no reason to notify anyone. Second, even if they did know that your daughter was doing this, there is no actual legal obligation on a lender to inform someone whose SSN or other information was wrongfully used that this happened--while the lender might choose to notify you, they are not required to do so.