Unfortunately I didn't capture a screenshot of this, would be rather complicated to do so.
I went into a battle with a pirate starbase with 3 ships. One of them showed in the tactical viewer as being destroyed, but my ship tally remained at 3 at the top. The shipyard didn't seem to fire any more weapons at my two remaining ships, and when I finally destroyed the pirate shipyard, the combat log showed it had continued to fire at my destroyed ship.
After the battle, the destroyed ship did disappear from the fleet. It seemed to be a combat viewer artifact.