For the greater good: Attempt in any system that contains a captured leader. If successful rescue that leader and draw 1 objective card. The leader(s) assigned to this mission remain in this system.

I'm assuming this means the assigned leader(s) stay in the system for the next round only or are they stuck there for the remainder of the game?

I apologize for the post. I found the answer in the rules reference (p. 12) Rescuing captured leaders.

I believe its just for the rest of the round, normally you have the option of moving the leader(s) that performed the rescue back to your base (the one you rescue always gets moved to your base).