This would imply a bug or exploit if you're right about the perpetrator: users get a pool of downvotes equal to 4x their karma (upvotes aren't capped), and private_messaging's karma is deeply negative. Given that I've heard downvoted users complaining about this behavior before, I think it's safe to assume that it's at least partly working.

private_messaging does have positive 30-day karma, so it may be indicative of a (presumably unintended?) lower bound on karma for this feature's purposes. Alternately you might be dealing with a sockpuppet with better public behavior. Anything more specific depends on technical details I'm not privy to; might be worth asking someone who knows.