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.