So throw them in the trash can when they're not lit?

lol I don't get that. If it's not safe to put something in a trash can, it doesn't mean you drop it on the sidewalk. Only with cigarettes do people think that way. With other things, it's obvious that you need to take the effort to dispose of it properly.

Does stepping on it put it out all the way? You could step on it, pick it up, and throw it out. Or pour water on it for good measure.

If there isn't a practical way to dispose of it safely, maybe it's best to not smoke right now, until you're near an ash tray or whatever. Or carry a disposal method with you (like a bottle with water on the bottom).