Unconditional love means that you will continue that love regardless of happens, whether the actions of the target of your love, or your own, or those of a third party. NOTHING can cause you to stop loving that person.
That being said, you can love someone without condoning their actions, a la "love the sinner, hate the sin". You can even love someone you don't know. Granted, that's not what people usually think of when you say love, but it's no less true.
It's much easier to love unconditionally if you actually understand (not just "know" in your head) that everyone is connected, so that you realize that you're just loving another part of "your" whole. It makes it much easier to simply let go of their actions, their "what", and concentrate on their "who"... which is really the only thing you can love, anyway.
Here's my expanded writing on this subject.