"Unfinished Men are Clay Men who lack something - sight, a voice, a hand, conscience, obedience. You can't really tell a crippled Clay Man from an Unfinished Man, except that ordinary Clay Men are never criminals. The distinction, unfortunately, often evades Constables and citizens alike."
"Some say that the essential thing all Unfinished Men lack is compassion. That it is the first thing to go. That's why their limbs begin to fall off, their senses to decay. 'That compassion is part of every Clay Man's fabric, that it is London that wrings it out of them."
Unfinished Men are exactly what they sound like - Clay Men who are missing something, as described before. A couple of notable examples of these are Jasper and Frank, who work as enforcers for the Masters. It's never been expressly stated what the pair are missing, though.
Unfinished Men are formed when the King with a Hundred Hearts has a nightmare. However, despite this start, and their unfortunate reputation, not all of them are bad, and a few may even be helpful.