It all depends on the content of the lease agreement. Typically residential leases do not automatically restart for another year, they convert to a month to month, but if the lease says otherwise then it could happen. You should have the lease reviewed by an attorney in your area.
As a guarantor, you are responsible for the lease as if you had signed it yourself, if your children are in default. You should speak with a landlord/tenant attorney here locally to understand your rights and responsibilities. In many instances, you may require the landlord to proceed against the tenant first and require them to exhaust efforts to gain payment from them before they proceed against you.
Responding to questions on AVVO does not establish an attorney-client relationship between the questioner and any attorney associated with Garrett Law Group, PLC. Responses should be considered and used for informational purposes only. Every case is unique in its facts, and all legal matters should be discussed with a licensed attorney prior to making any decisions or taking any actions.