Yes, it's actually possible for a bankruptcy to be reopened. A Chapter 7 bankruptcy case can be reopened after discharge and case closure under certain circumstances. Bankruptcy Code Section 350(b) authorizes the bankruptcy court to reopen a case for various reasons including to "administer assets, to accord relief to the debtor, or for other cause." Fed. R. Bankr. P. 5010 states: "A case may be reopened on motion of the debtor or other party in interest pursuant to §350(b) of the Code." . See In re Chalasani, 92 F.3d 1300, 1308 (2d Cir. 1996).
Ultimately, however, the decision to reopen is within the discretion of the court, and merely granting a motion to reopen does not afford substantive relief but simply provides the opportunity to request further relief.