Hilary (apologies if this address is wrong), 

as you know the possession number determines the use of plural or singular ‘possessive adjective form’  in French. 

When there are multiple possessors, each with their own unique possession the usual approach (idiomatic) is to use the singular possessive adjective with the possession also in the singular.

Therefore, in this case as each actor has their own individual and separate career, it is ‘ leur carrière ’. 

Using the plural form would suggest either that they all had multiple careers, or had shared ‘ownership’ of a set of multiple careers. Whereas the singular does not directly cover the possibility that one or more of the group, but not everyone in the group has (had) multiple ‘careers’ (or whatever other possession could be in consideration).

Yes, it is ambiguous without context/further explanation, which would be expected to be known or given when necessary ! 

English has difficulty in this regard to - eg ‘ they love their cars ‘  tells you there is more than 1 person and more than one car, but not the division of ownership of cars between them.

See attached from Laura Lawless under ‘ the tricky part’ and especially ‘ the really tricky part ‘ :

 https://www.lawlessfrench.com/grammar/possessive-adjectives-plural-possessions/

Maarten,

Thank you very much for your explanation. 

I read Laura's lesson, and the two of you together helped clarify this question for me. It is a little hard to wrap one's head around, ie. the use of the singular possessive in the third person plural, but Laura points out that it's idiomatic, which is instructive. 

My understanding is that the third person possessive adjective "leur" is used in the plural when each person possesses more than one of the items. Laura's examples are: "Il veut leurs idees."; and "Ils aiment bien leurs profs".  In the first case they each have more than one idea, and in the second the students each have multiple teachers. 

To sum up: The use of the third person plural possessive adjective, "leurs", requires multiple owners each of whom owns more than one of the items. I came up with the following examples:

 "Les pilotes de course aiment beaucoup leurs voitures." ('pilote de course' = 'race car driver') In this case all the race car drivers have several racecars. 

And, "Les petits enfants perdent toujours leurs chaussures." The children each have more than one shoe.

It will probably take some time to get used to when to use "leur + singular item" and "leurs + plural item", but this has certainly been a great help.

Merci Beaucoup ! 

(And, yes you can address me as Hilary (It's my middle name and that's what I use.)

Bonne Continuation !

In the case of "Il veut leurs idees", I think this needs a plural even if each person only has one idea, because it's seen from the perspective of a different person (il).

Alan, 

Alors la !  My brain is starting to short-circuit! 

You make a very good point, though. And, Laura discusses these types of grammatical nuances in "The Really Tricky Part" of her lesson. (link above in Maarten's post) 

By the way, how would one say, 'short-circuit' in this context in French? (That is in connection to my 'brain' short-circuiting' as an idiom.) 

I researched it: "short-circuit" = "court-circuiter", and other than the electrical definition, it is used to refer to 'bypassing' someone or something. 

From Robert's: familier: Laisser de côté (un intermédiaire normal) en passant par une voie plus rapide. ➙ anglicisme shunter. Court-circuiter son supérieur hiérarchique.

In any case, this has been a fun and informative discussion.

Merci beaucoup et bonne continuation !