You had conjectured that Callista gave the DeKocks a hostage, and Board Member #7 has been absent the entire game, but in a way that Yvette is determined to keep an absolute secret, so he/she is clearly not "just busy". During this vulnerable time for the company (as described in the Phoebe-Yvette-Elena scene), this is the worst time for a key decision-maker to be absent, and to allow your enemies inside one of your secret facilities (and the most important one for determining your company's future), yet both cases are the status.
Why? What would possess the Board to invite DS at this time? DS leveraging a hostage would certainly make sense, and KG counters with Kane as their own hostage (as Cole is secret even from the Board), thus DS limits their maneuvers to not jeopardize Kane. Cole, Callista, and Astrid cannot be Board Member #7 as their living status are official secrets from other Board members, neither is any of Phoebe's family, nor the DeKocks, else they would have been identified at the Welcome Party, so #7 must be someone we haven't met yet. A kidnapped Board member is definitely not something Yvette will openly admit has occurred, even in front of the perpetrators (look to Cynthia for example: who never accuses KG of holding Cole prisoner, even though she knows they are, instead arranges to locate/rescue him without their knowledge). It’s possible, one of the motivators for Callista faking her death was to be able to pull off the kidnapping. ... perhaps #7 is even Callista's/Cynthia's source for discovering that Cole was alive and still imprisoned (Nadia should have stumbled across his location before realizing he was alive if hacking was the information source).
