Assuming it is in good standing, your account would be terminated (and your postpaid plan) once all outstanding dues are settled.
It goes without saying that some postpaid plans are terminated (but not the account) because of non-payment but the accounts are still held active or archived because of its continuing liabilities which globe hopes to collect.
You may request for the termination of your account. But you need to pay applicable charges.
As for your your question if you need to pay your outstanding balance. Yes, whether you will terminate your account or not.