I've got just this one issue of Supergirl's second self-titled solo book. I don't remember how it came into my possession. My best guess is in some random grab-bag of comics I picked up at a grocery store or something like that, but it may have been part of a gift from a family member that just knew I liked comics.
This issue is essentially the second part of a story that started in Superman. Supergirl follows some alien spacecraft to Metropolis and finds Superman tangling with the Kryptonite Man. His people species lived on Krypton long before, and were in hibernation when the planet blew up. The mountain he was in was thrown clear and turned to Kryptonite, which his body fed on. He thinks the later Kryptonians made the planet explode, so he wants to kill Superman. Supergirl's basically a throw-in, since he didn't know she existed until she gets involved.
There's also some mysterious group of aliens after the K-Man for stealing one of their ships, and they've booby-trapped it to kill him. They talk of themselves as some big wheel, the unknown movers and shakers in the galaxy, but they're played as a bunch of losers. Their played as indifferent to the lives of anyone other than themselves, to I guess make the K-Man look a little better in comparison.
I don't guess it's representative of the book as a whole, given no members of Supergirl's supporting cast appear, nor are there any updates or even allusions to any subplots going on in the book at the time. Of course, the book ended 2 issues later. Then Supergirl was killed off in Crisis on the Infinite Earths. Then DC decided they wanted to go back to Superman being the only Kryptonian, so no cousin that also survived (no Kryptonite Man either, presumably, unless you count Metallo.) That didn't mean they were satisfied keeping the concept out of circulation. . .
