It is not actually building the ships. It just shows the wrong result (it ought to show some really large number of turns, depending on how you handle dividing by Zero production to get how many turns it will take to build a ship there) for how long it will take to build ALL of the designs when I look inside the Shipyard, i.e. I was in one of my Shipyards and I was using the left or right arrow keys to step through all of my shipyards, when I noticed this oddity in that particular Shipyard that lost it's Core World sponsor.

I have warships and transports on the way to take back that Core World from the Alien Race that took it from me. I lost control of that Core World several turns ago.

I am trying to kill off the Xelosi completely. I have captured all of their planets, including their HW. They only have one star base left, that I can not find in the star system that matches the name (or in any other system in that Sector), in fact, I have a Star Base in that star system that matches that name. So I strongly suspect that they have a LOT of small, i.e. Tiny, and a few Cargo Hull ships, and they are all hiding in the Shipyard that belonged to their Home Planet, which I have captured. That shipyard shows as having 200 hit points but only 3/3/3 for weapons and 0/0/0 for defenses, and if I choose my main warfleet in that Sector and then put the tooltip over that Starbase I get told that I can NOT win a battle attacking it. I want them to die, instead they keep offering me a Peace Treaty. which I refuse.

When I use the Diplomatic/Trading screen, I can see a list of their 60 or 70 plus ships, by name and design, i.e. their attack and defense ratings plus hit points and speed. The problem of them refusing to die off, apparently, is that they could still come back to life, since they have at least one Colony ship, and/or they could capture a small colony somewhere.