First and obvious answer would be that at the time you’ve paid your payable and the other party has no remaining receivables against you. 

When in truth that’s the most obvious one and most common of course, there are other circumstances when you can / should derecognize a payable.

Another reason to derecognize a payable is when your supplier says they don’t want the money anymore for an example. Your supplier or any other party you’ve got the payable against, i.e. if the tax is no longer collectable or the employee you had bonus obligation against, gets fired and doesn’t have the right for the bonus any longer and so on.

In case you’ve taken out a loan and it gets refinanced, you also should derecognize the old liability and account the new one. The same may apply if too many of the conditions change for your existing loan liability, i.e. the due date, the interest rate, etc.

Also, if you’ve accounted for a certain liability because you either got some goods or services and are still waiting for the invoice, the liability is obviously an accrued one. Normally, if you’d receive an invoice for it, it would move to accounts payable and that’s the end of it. However, in practice your supplier may forgot to send the invoice and eventually let’s say go into bankruptcy, what you can do with your payable is after a certain time period has elapsed (normally given in your local legislation), you can account this payable into your income (since initially it was expense).

So as you can see, there are many circumstances when a payable is derecognized from a balance sheet.