This is a question I was asked recently in my Q and A. The tenants had run up a large rent arrears debt and then absconded. The landlords wanted to put in some new tenants but were worried that doing this might cancel out the original tenants’ debt.
Happily for them, my reply was that re-letting the property would not affect their liability for the current rent arrears at all. So long as the landlords were absolutely certain that the previous tenants had left (and you can read a bit more about this here) re-letting the property to someone a bit more reliable was the best thing they could do.
The effect of the new tenancy agreement would be to end the previous agreement (assuming it had not ended already), and the former tenants would not be liable for any rent after the new tenancy agreement was signed.
They probably wouldn’t be liable for rent after the landlord had re-entered the property and changed the locks, as in an implied surrender situation, the landlord by doing this will end the tenancy.
However in neither case will the landlords actions affect the rent arrears already due. The former tenants will remain liable for this and (if the landlord is able to find out where they are now living) he can sue them for the whole sum plus interest.