The ending of the film was left intentionally vague by the director, Morten Tyldum. In short, he's happy for you to imagine that they went on to have kids, but only if you want to.
We had a longer ending with Andy Garcia walking out of the elevator.
'Why is he in one shot?' Because it was two scenes that we shot with
him, but we find out that by doing the ending a little shorter, it
made people talk more about it. I want to like, 'Did they have
children? What happened?' It's good. Somebody will go like, 'Oh, I
think I saw some children inside the house.' Somebody goes like,
'Wait, if you saw that, then there probably is!' 'How was their life?'
But they both get to do what they set off to do. She set off to write
a story. She thought it was different story. She had to, instead of
looking outward, she had to look inward... Which I think is amazing,
and he build his house, and was able to live in it... So, in many
ways, they completed what they needed, and the rest I want people to
imagine and talk about and it should be up to them.
'Passengers' director defends the movie's controversial ending
By contrast, in the film's original script, the ending was far less ambiguous. They had kids and even made use of artificially inseminated sperm along the way.
The ship’s hull is scorched and abraded from its cosmic crossing. But
the lights shine, the engines throb, the landing gear receive the
weight of the ship.
The starship’s gangway lowers. The doors open. CHILDREN run down the
gangway. Children of all ages, of all races. Twenty of them, thirty.
They point at the sun, at the clouds, laughing, wide-eyed in wonder.
We move up the gangway, through the disembarking passengers. Behind
the children: Teenagers. Adults in smaller numbers as they grow older.
Finally a handful of gray-haired elders.
At the aft end of the Concourse, a high wall. Here a long list of
dates is inscribed. The last date is the ship’s landfall on Homestead
II; the first, Jim’s awakening. In between: an accelerating tally of
births, deaths, marriages, catastrophes and achievements...a century
of shipboard life.
Which was a necessity because they'd
accidentally vented all 5000 of the other passengers into space.