I am currently living with two other people. We have signed a 12 month lease and are only four months in. One of my roommates has decided to move out. Our lease requires a written statement signed by all tenants if one or all want to move out. The two of us have thus far refused to sign him off the lease because he has late bills he needs to pay. We have stated that once he pays all his bills we would be happy to let him leave. He refuses to pay the bills and has decided to move out anyway without being signed off the lease.

Legally, what are my options? Because he's decided to abandon the place, we are left with any and all fees required to get another tenant to take his room and we may be held liable for any damages he may have caused.

... Legally, what are my options? ...
You and the other remaining tenants can sue him according to what appears to be lease provisions making him liable to you. Although you are still liable to the landlord, it appears that you have a sort of subrigation claim against your former roommate.