If the source of the condition cease to exist, is the condition style valide ?

Example, if I give someone the "I'll Show You The Dark Side" condition and later on, the ship with Kylo Ren crew is destroy, what happen to the condition card ? I see no reason for it to disapear, I would think that it would just stay there until resolved.

Yes, there's no general rule about when Conditions are discarded (well, I guess except when the targeted ship is destroyed), so it sticks around until it says otherwise.

That's what I thought, but sometime you just miss a rule somewhere when you try to figure out something

The Suppressive Fire condition specifically mentions that it's discarded if the ship that assigned it is destroyed. Stands to reason that if that was the intent for I'll Show You the Dark Side, the card would specify that as well. And if it were a general rule, Suppressive Fire wouldn't need to state it.

Suppressive Fire may state it.

ISYTDS stays until triggered.

A score to Settle giving A Debt to Pay may stay but won't do much when the matching half leaves play.