I'm not sure that I agree with this. I've seen several *sshole characters that I (and others) have felt sorry for. They might be jerks or even scum of the earth, but if something happens to them that's absolutely horrible and it devastates them, that could very well invoke sympathy. I guess it depends on how deep the dislike for the character goes and how sympathetic the reader/viewer is.
To sympathize with characters, first and foremost is the character needs to be likeable. If we don't like the character and bad stuff happens to him or her, we won't feel sorry for them in the least, sometimes even if he or she does or does not change their ways. This is one of the many warning signs out there that you aren't writing a good character when no one feels sorry for them. It would make sense if the protagonist is a heartless jerk and karma bites them in the butt (in which case, why are we cheering for the jerkish protagonist in the first place if they refuse to do a heel turn?), but if they aren't, then you're writing the character incorrectly somehow, and the sympathy is lost on us.
I'm also not sure that I agree with the notion that a character is bad because they're unsympathetic. Sometimes there just need to be characters that exist to be hated. That doesn't necessarily mean they're bad, as they can still have depth to them. If you're talking about the protagonist, then I agree that they should have at least some redeeming characteristics or else the audience will be rooting for the villain to win (unless the villain is much worse and you're sort of stuck between the lesser of two evils, but I digress.)
Anyways, it is possible to feel bad for both parties, but it takes tact to pull off correctly. Sometimes, one character will appear more "in the right" than the other, so if you're trying to go for equal sympathy, then you need to make sure you find a careful balance.
Claimed: Grovyle - November 10th, 2013