Can evil characters engender sympathy?

Yes, defiantly "evil" characters can engender sympathy. But it has two way of thinking about this. Sympathy to the "good" or "evil"?

Sympathy to the "good":

It depends on the situation that happen to the "evil". I believe that all human beings can engender sympathy to others, so does "evil". One is going to ask, "if that person is an 'evil', and 'evil' is usually bad, how come 'evil' will do the right thing?" First, "evil" does not stand for 100% bad, maybe they got that "title", even though they did something wrong only once in their life. Second, "evil" might just think differently with us, which does not mean that they are "evil" or they did something wrong in their life. For example, if a series killer is not killing a person one day who he loves, his love might persuades him to stop, the killer might go to admit his fault, and go to the police office.

Sympathy to the "evil":

There are always "evil" engender sympathy to the "evil" side. If two are friend, one does not want to do bad thing any more, but the other one cannot stop. One would ask the second one to stop, however, the second one won't stop killing people and giving lots of excuses how he cannot stop. The one might accept his excuses and "cooperate" with him. Then, that's kind of sympathy to "evil".