The answer to the question will lie in your operating agreement (you did have one didn't you?). Typically a well-drafted operating agreement will treat a bankrupt stakeholder in such a way that he or she no longer has any rights to control how the LLC is conducted, and will instead give them an interest that the other stakeholders may be required to buy out, but on an installment sale basis at a low rate of interest over a long period of time. If the agreement is in place and it has that sort of provisions, the question will become whether you and the other stakeholder can meet those terms.
If there's no agreement, you need to look to your state's LLC statute ... probably the court will be able to force liquidation.
