[Casiopea]

Well, it's ambiguous. The reason being, people can have more than one job:

[1] Max and Pat lost their jobs.
=> Two people, two jobs each.
=> Two people, one job each.

Consider something like, parking a car:

[2] Max and Pat parked their cars. (Two people, one car each)

Note, it's physically impossible for one person to park two cars at the same time, so the meaning expressed in [2] is, Max parked her car and Pat parked his car.

Without -s, [3] below becomes ambiguous:

[3] Max and Pat parked their car.
=> They came in the same car, and one of them is parking it.
=> They each have one car, and each of them is parking it.

Context is important. I agree with tdol. Try to disambiguate the sentence, e.g.

[4] They lost their jobs at tha plant. (Many people, one job each)
=> They each had only one job at the plant.