How about the version I call Mr. or Ms. "Everything Is Wrong," or sometimes, "That Won't Work Because..."? I know someone who is like that at least partly because she's perpetually depressed, but that doesn't make it any easier to deal with... she always has fairly serious practical problems in her life, such as: being evicted; losing her job in such a way that she can't collect unemployment (e.g., being persuaded to submit a resignation letter when actually she was being laid off); not getting child support, but not chasing after it because she never bothered to get a court order for it; working an under-the-table job that pays so badly she could qualify for food stamps, yet not getting food stamps because they require proof of income, which the under-the-table-job can't provide; etc. (insert relatively serious, intractable practical problem here). She's a single mom dumped by the dad, exactly the kind of person that government programs were designed to help, but she seems to have actually chosen to fall through the cracks (she would qualify for medicaid, but doesn't bother to get it, etc.).
The reason I think of her as sort of an energy vampire is because every piece of good advice you offer her seems to interest her--so you offer more, whenever she needs it, which is every time you see her--but she never follows through, and her life remains terrible. She always responds to advice with something like "Huh, well that would be great... although I can't really do that, because [ludicrous reason that it wouldn't work]." It soon reaches the point where you can sense that if you keep talking to her, you're going to get depressed and a little angry... angry at her, for not trying to make her awful life a little better!
I've known a few people with varying degrees of this odd syndrome. Depression, negativity, what have you. I don't know how to handle it, other than avoiding them or encouraging them to get real help (e.g., antidepressants, counseling, whatever).