Can evil characters Ingender sympathy?

I think that evil characters aren't always 100% evil and have a soft spot. In certain movies or stories I've seen, certain villains do show some sense of feeling but don't want to show it, and believe its a sign of weakness. Evil characters want to be seen as powerful and cause demise to other people, and if they are seen as too sympathetic, they probably believe that it will effect their image.

Examples of sympathy can include, when characters may not go through with a plan that would cause catastrophic results and maybe even tone it down. When an evil character is complemented for showing some sort of sympathy, they may brush it off and say that it was nothing and still insist that they are evil. So it may be apparent that deep down inside, they really do feel something but can't or don't want to show it on the outside. Evil characters may even begin to show some sort of sympathy, but then realize what they are doing and suddenly force themselves to display evil once again. So in summary, I do think that evil people can show sympathy but it doesn't show too often unless you analyze the person carefully. They probably hate being seen as nice or sympathetic person because they want the title of being evil, and status or how they are viewed is probably prudent for them.