A thought on character plots.

Given recent events in certain stories that I have invested my time in, I came across this sort of fascination with a type of plot that I haven't seen used too many times.

Have you ever followed a character, possibly not fully because of their personality, but for their beliefs? When a character is devoted to something happening, you can relate to what they're trying to accomplish, and hope that they succeed.

Game of Thrones does this trick well, where you follow a character for what they're doing, but not necessarily how they act. My point, which I am not getting to at all, has something to do with that.

Recently, (Not naming any names) A character died in Thrones, which happens a lot, but once again not the point I'm getting to.

Some stories simply end an ideal when the character fueling said ideal is killed. My question here is;

Would you as a reader still be interested in what a character is trying to accomplish after their deaths? I get this happens a lot in real life. I am not talking about real life. In the best stories, there is a metaphorical meaning to characters, and what they try to do with the world around them. If the character dies, and other characters pick up where he/she left off, would you still feel invested in that? Or are you more interested in the classic story feel to it where a character's aspirations are his own? Should a character die with their cause, or do you like the idea of the character's struggle living on through others?

Sorry about the way I write. it's secondhand to write all mystical now.