I had a handful of ideas for this jam. I won't be able to develop all of them to my satisfaction, and some aren't even half-baked, but I figured I should put them out there to see if they spark something for anyone else.
1. A game for two players: Two ships are travelling together on a course that will take them a century or two to complete. They can communicate on a private channel but only at a rate of one letter per year. They also know that they'll be repurposed and separated upon arrival, and may or may not be able to have one last contact upon touchdown. (Neither player can say anything while the game is ongoing, and need to react to the other's message in real time as it's being sent out.)
2. A creation game, for solo or group play: The humans living on the generation ship need to undergo mutations in order to survive their arrival on the new planet. An entire generation is played out in a single round, where three things happen during this time: a physical mutation appears, a change happens in the social order, and the ship creates something new to stimulate the community. These three changes are decided through dice rolls, and you write out how they play off each other to change the community as a whole. Repeat this for 5/10 generations, at which time they arrive at their destination. What kind of world will they inhabit? Are they in good shape to do so?
3. A creation game, for solo or group play: The humans on the ship are in stasis, and the ship is on the lookout for interesting space phenomena to use as the basis for mental stimulation in the form of dreams. Unbeknownst to the ship, these dreams will become a foundation myth for the new community, with each phenomena being interpreted for each of the following roles: the starting state, the people, the event, the action, the ending state.
4. A slime infestation requires forceful intervention by the ship's robot maids.
5. Different sections of the ship end up isolated for 500 years by massive bulkheads, with each developing in a radically different way. When the bulkheads open, everyone can re-acquaint themselves and adventure as desired. In my head, the setting resembles Septerra Core, an old CRPG.
6. Internal farms are maintained by a robotic workforce in order to provide fuel for the ship. Routines are quickly established, but over time the robots degrade, requiring them to adapt themselves and their routines to continue the cycle. A more melancholic vibe, though I have no clue how to convert this into mechanics.