If you signed the lease extension thinking it was a month-to-month renewal, then there is not much you can do about it now. Be sure to read every word before you sign a document.
The apartment complex should have tried to re-rent the unit after you left if they chose to take the premises on your account. You can ask to see if they were able to re-rent it and if they did, you shouldn't have to be on the hook for the amount of time it was rented to someone new.
You can write to the collection agency and demand proof that you really owe the amount they say you do. You can also write the apartment complex and ask when they re-rented that unit. If you can, visit and ask the next door neighbors who remember you if the unit was re-rented.
If you find out that the premises were re-rented and there were no physical damages and no balance owing for unpaid rent, you may demand that they return money to you. See a local lawyer if you are unsure. Good luck.Ask a similar question