With the third person plural possessive structure...

The possessed loses the "-k" ending and will look like the singular third person ending, except when:

• the possessor is not named:
  "a házuk" - (their) house

• the possessor is the pronoun itself, "ők". But "ők" will lose its "-k" ending instead:
  "az ő házuk" - their house.

In all other cases, the "-k" ending is lost:
"a zeneszerzők háza"

This is true when the possessor-possessed structure is not "broken up". For example, by a predicate (a statement). Like "nincs". Where there is something in-between that is not just an adjective (like "a zeneszerzők piros háza"), the structure is broken up, and the "-k" ending returns, let's say, to make things clear.

So, in this case, I believe that the correct version would actually be:

"A zeneszerzőknek nincs házuk".

But the above is a very common mistake in the living language.

We don't usually use the plural here. "They don't have a house" would be for example "Nekik nincs házuk", or simply just "Nincs házuk", but noone would say "Nincsenek házaik". It would be suitable only when you want to dramatically emphasise that there are many people without a house, for example after a serious cathastrophe.