I am still not sure of what you mean by 'stopping the unpaid'.
The All tab shows Paid, Unpaid and Draft invoices. This is not like a recycle bin, it is an important list that shows all of the invoices in use.
If an invoice is not outstanding (outstanding means Unpaid), it is Paid and will, therefore, display in the Paid (and All) tab. To pay off an invoice, a transaction must be allocated to it. You should pick only one of the methods below, to do this.
If you are importing transactions to be explained
Bank Explain screen overview
If you want to create a single transaction for an invoice ('The alternative approach' at the bottom)
How to record cash transactions
If you don't want to bother matching your bank account
How to Quick Pay an unpaid invoice