They could have both lived to see Homestead II
At the end, once they figured out about hibernating in the Autodoc, they should have decided to share it, one at a time.
Person 1 goes in Autodoc for hibernation, Person 2 lives for one year alone, wakes up Person 2, have one romantic day together, and then Person 2 hibernates in the Autodoc for one year.
They will only have aged 44 years by the time the ship got to Homestead II.
During their time alone, they could write a journal/record video diaries, and the other person can read/watch it during their time awake.
I also feel the loneliness wouldn't be as bad since you have that one day of romance with the other to look forward to, not to mention actually getting to see the colony planet at the end.
If anything happens to the person awake, and they need to use the Autodoc for medical treatment, they can wake up the hibernating person any time to do so. If the awake person dies, then the hibernating person would just remain hibernating until the crew wakes up. Seems pretty foolproof to me.
The only other theory I saw that was similar was this:
https://www.reddit.com/r/Passengers/comments/6458wj/hacking_the_ending_earth_by_55/
But in that situation, Jim and Aurora would be splitting their time evenly (awake, asleep, together) and would have aged 59 years at the end (if both of them would even live into their 80s-90s). I don't think that's an ideal situation for anyone.