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If your name being added to the tenancy is with your agreement and you are or were living at the property, then yes, it is legal. A tenancy agreement does not have to be in writing it can be verbal and even a persons actions can be considered as having a tenancy. Even if you don't sign you will still have protected tenancy right that are inferred by you being there.
That clause is very normal and applies often.
You would be legally liable for the duration of the tenancy contract for you part until the agreement ends or you find a replacement.
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