They won't just stop collecting taxes. In fact, what they do is, they focus on collecting taxes, including keeping all overpayments, and only later work on processing claims for refund.
As a result, if one has had too much tax withheld from one's pay, a refund will be a long time coming.
Furthermore, if one has an overpayment from one year that is supposed to be applied to the next year, that may not happen if the earlier return hasn't been processed yet - they have been known to process the returns out of order - with the result that a false underpayment will appear on their records and they will start dunning you for the underpayment.