Traits are things you've either learned, or were born with. It would be utterly illogical for you to forget/lose them just because the club went out of business.
Aside from the logistics of when (as in, could your character have learned it before it went under) he would've learned it. An established character would not lose the trait. If the cannon dictates that the faction would've gone under before your character would have learned it. I would ask you to change it. If your character is of a vintage where that would not be an issue, Zhaynes comment stands.
You could also just reflavor and rename the traits to be whatever.
You could also just reflavor and rename the traits to be whatever.
I don't know if it was asked with pfs in mind so I didn't want to presume that option, but yes, considering that the faction might have failed. It would not mean the end of varisian crime it would only require a very small alteration