If you sign a lease agreement as a cosigner and not a separate cosigner agreement and are verbally told that it will remain in effect for 1 year after that you are not liable, then the person you cosign for never ends up signing a new lease after the year expires but ends up behind in rent and gets evicted from the property are you then in turn responsible for those charges?

This is a difficult situation. It depends on the language in the lease. Was the lease for a 1 year term? Did the lease provide that it would automatically renew for 1 year or would it become month-to-month? When you signed, did it say co-tenant or guarantor? Did you ever give the landlord written notice that you would not be responsible after the 1 year term ended? All of these things will affect the result.

Basically, if you signed the lease as a co-tenant, and if you never gave the landlord written notice that you would not be responsible after the completion of the 1 year term, then you are going to be responsible for the unpaid rent and any additional charges such as legal fees for the eviction, damages, etc. If the lease provided that it automatically renewed for 1 year periods then you are also going to be responsible for rent until that current term ends or until the landlord re-rents the property.

As Lisa said, it is very possible you can be held liable, this is why you never co-sign on any loan or rental you are not able and willing to pay. It is possible that the lease turned into a month to month or renewed, anything verbal said not written on the lease can't be upheld. So you needed that statement written into the lease.