Unlike many Greek poets, we have quite a lot of Theognis, with many manuscripts to work from. Since most of what we have is gnomic (wisdom) poetry, it is commonly assumed the texts were copied because they were thought to be edifying. One result of this is that other lines thought wise or clever made it into the textual tradition, and a large number of the lines attributed to him are not work Theognis at all.
Other poems are listed by the Alexandrian librarians, but we have none of them.
Theognis is aristocratic in his sympathies, and when he talks about the κακοί he's as likely talking about commoners as he is about people of iffy morals.
Tyler, on pages 22-23, says, "His verses were addressed to one Kurnos the son of Polypas, of whom nothing futher is known than Theognis suggests. His lines contain frequently very excellent moral maxims, and for this reason were studied in the Greek schools as part of the moral training of the young. He was, however, a disappointed, embittered man, and his feelings are constantly coming into sight."
The Tyler book omits most of the later poems, which are frankly erotic in the Greek Aristocratic mode.
The Suda says this about him.
Texts are checked against M.L. West's Iambi et Elegi Graeci.