LaserPro is correct to warn you about a potential problem down the road. Here's the issue:
§202.7(d)(1) of Regulation B prohibits lenders from requiring signatures of anyone (on any credit instrument) that is not applying for a loan. If you have the parents sign an unlimited guaranty, it basically states that ALL debits (forever) will be covered by this guaranty. IOW, it attaches itself to all future obligations.
Now, let's fast forward a year down the road. Let's assume that this individual comes back to your bank to buy a car in her/her own name. On the surface, this person can't get individual credit because the unlimited guaranty attaches itself to this car loan. The parents are also liable for this loan. Therefore, the bank has violated §202.7(d)(1) on the new car loan.
How can you have the guaranty and not violate §202.7(d)(1)?
1. Make it a limited guaranty that is only applicable to a specific debt or a line of credit, or
2. Cut the guaranty off on all future, non-applicable obligations. This is difficult to administer, but I have seen a few banks do it. Basically, if a loan is made to one individual where the Equal Credit Opportunity Act would prohibit the use of the guarantee, the note for that loan should state "this loan is not secured by guarantee dated ??/??/??" in the collateral section.
I have seen several banks use unlimited, cross guarantees between spouses for farm or commercial loans. I have also seen a few of these banks get very badly beat up by their regulators for this practice. This is a severe fair lending issue (requiring spousal signatures) if you don't handle it correctly.
Good luck.