No, you should not be responsible:1) Tenants are only responsible for damage done to their premises by people under their control--which you state your ex-husband is not (e.g. he was not invited, was not a guest, is not living with you, etc.--if , however, he was a guest or is living with you, then you would be responsible). If you become involved in litigation with the landlord over the money, you'd need to be able to show that your ex was not under your control at the time of the incident.2) If you are the victim of domestic violence, I believe the Violence Against Women Act (VAWA) prevents the landlord from charging you for damage done by your attacker.Suing your ex-husband may be the landlord's proper recourse.