"His work came to nothing" = all the effort, or work, that the person did, didn't produce anything worthwhile. That all his time was wasted. "His work went to nothing" is not an expression I've ever heard used.

I agree. 'His work came to nothing' means that it wasn't successful or that the result of his work was not worth the effort. 'His worth went to nothing' does not mean anything.

I second what Michael says. I think "His work came to nothing" is an expression. If you look at the terms "came" and "went" literally, it goes something like this: Came usually refers to something/someone that was far away from the speaker and has moved closer. Go/went usually means that something/someone is near the speaker and moves farther away. I am by no means an expert in English so someone else may correct me if I'm wrong :)