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This issue will be resolved by the terms of the "mailbox rule" - meaning that your offer to renew the lease was accepted by the landlord in writing through the letter. Whether or not the acceptance is valid depends on whether your withdrawal of the offer happened before or after they sent the letter.
This means that you must look at the postmark on the letter - if it is dated before your notice to vacate, the landlord can hold you responsible for another 6 months (you may be able to argue that it is invalid due to a lack of signatures etc., but this is not a terribly strong position).
If the postmark is for after your emailed notice to vacate, the landlord cannot hold you responsible. You withdrew your offer before the landlord accepted.
I hope the above is helpful, if you have any questions please do not hesitate to let me know and I will follow up quickly.
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