Why do I see "unpaid invoices" when trying to close my account?
An error message says you cannot close your account because you have unpaid invoices.
You either have unpaid Previous Invoices (which you can pay from your Pay Balance page), a Pending invoice (scheduled to be charged soon), or a balance for the ongoing month (scheduled to be billed on the next month).
Should you have any ongoing charges, you first need to remove your paid services or delete the applications running paid services, either of which can be accomplished from your Heroku Dashboard or the CLI (as you prefer).
Once that's done, you can use the Remove credit card feature on the billing page to expedite your final payment. If you have any remaining ongoing charges, this feature will let you know what apps they're stemming from.
When your final invoice is paid, you can proceed with closing your account.