The title says most of what the side-quest would be about. Recieving a distress signal from a civilized planet/space station after a period of time provided some requirements are met - enough NPCs, certain tier gear etc. The results on arriving to the source of the signal can vary with the time it took for you to arrive. Minor losses on the planet/station if you arrived less than a day after the signal is recieved, heavy losses but redeemable if you took longer - the severity will increase with more time, and finally destroyed/overrun/enslaved if it takes you a week to arrive - should you arrive - and you will automatically fail the side quest if this is what happens. Once you have arrived, you will have to destroy the invader's flagship/kill their leader or something similar. Your reward would, ideally, be an alliance with the saved civilization as well as an NPC. Dying on the planet/station/enemy whatever causes you to fail. EDIT: Sherbniz raised an excellent idea. Hostiles could send a fake distress signal to lure you into a trap! The reward would be... Whatever the hostiles are carrying, really.
I like the idea of distress signals, it's a very athmospheric and dramatic way of discovering an alien civilization! Following those should sometimes lead to abandoned ships full of enemies and treasures, or just long-deserted planets that the players can explore and salvage!
Hmm interesting idea and something I've been thinking of as well, you seem to have covered the bases on what to find from actual people looking for help to it being a trap set up by hostiles.
What about giving the player the ability of sending out a distress call to initiate a contact with another spacefaring civilization? Ally, neutral or hostile? It all depends on what you roll. You could actually request supplies or repairs this way if you're stranded somewhere.