LLC Bankruptcy - The LLC is a legal "person", distinct from the LLC's member, which would be you. It has standing to file bankruptcy if that is advantageous. Setup entities, like s corporations, corporations and LLC's, only get a discharge of debts in Chapter 11, which is prohibitively expensive. If an LLC files Chapter 7, it is shut down and any assets may be liquidated by the trustee.
LLC Bankruptcy - Your Exposure
Your personal exposure depends on how you have handled the debts of the LLC. Since it is a separate legal person, you are liable for its debts only if you personally guaranteed the debts, are made liable by a statute, similar to the one making officers liable for unpaid employment taxes; or are liable because you have failed to keep your personal finances separate from the entity's. Piercing the Corporate Veil.
A bankruptcy lawyer can help you set a course to deal with the situation.