I got this report from a library:

When items age to long overdue lost, they assess a fee equivalent to the
replacement price of the item.

That makes sense.

When those items are checked in, the fee is removed and the titles no longer
display as checked out. The overdue does remain in the patron's history under
fines.

That also makes sense.

However, if we renew one of those items, it assigns a new due date, but does
not remove the fee or the long overdue lost designation.

And, if we take payment on the item, it balances out the fee, reducing the
amount due accordingly, but the title continues to display in the list of items
out as long overdue lost. The result of this is that our staff members continue
to mention these overdue items to the patron even after they've been taken care
of.

Other categories of lost - those that are manually set - remove the title from
the list of items out.

Renewing an item should also remove the fees and the long overdue designation.

And paying for the item should remove it from items out and show it only in
payment history.