Once inside the chamber, Bucky keeps the ONE COMPUTER OPERATOR at bay with his big gun (hee!) while Syd searches for something on the 'puter. I think she's supposed to be attempting to access the system that operates the cryogenic stuff, but she's wasting time looking for her mother's name. She looks up "Laura Bristow" and finds nothing; then she looks up "Laura Derevko," which is either Spy Mommy's alias or her actual name, and finds a whole list of pertinent things. Like zeros and ones and other digits that mean ABSOLUTELY NOTHING. Seriously. It just looks like she finds some bloody binary code or something.
Bucky tells Syd to get the lead out, so she quickly disengages the core. Or something. She enters the chamber, does some shit with a temperature box or something, and nabs the core. At the same time, more of the Kasineau baddies show up in the upstairs office and discover their downed compatriots. One of them hits the alarm, which causes Bucky McBuckerton to turn away from the computer guy for a split second. That split second is all the computer guy needs to launch himself at the keyboard and swing the transport arm into Sydney's head. Bucky knocks him out with the butt of his gun just as Syd hits the floor.
She's fine, but her mask is cracking, allowing the subzero temps to toss her into the deep freeze. Unfortunately, the alarm has caused the system to go into lockdown, so Bucky can't get to her without shooting the hell out of all of the surprisingly non-bulletproof glass. He gets to her, swoops up Sydney and the core, and, instead of worrying about the baddies that are most likely going to show up at any second, he drops Syd on the floor outside the cryo chamber and tries to revive her. Of course she comes around just as the one of the baddies makes his appearance. Bucky disposes of him quickly, and he and Syd make their escape.
Back at The Institute For Idiots, Francie and Willage are discussing the infamous ticket stub. They're all, maybe she's having an affair with someone or maybe she's in an abusive relationship or maybe she's having an affair with her boss or maybe she's having an abusive affair with her boss. Whatever. End scene. Seriously. Just shut up.
The Best Little Safehouse in Kasineau Kountry. Syd's bundled up with a cup of hot broth. Bucky enters and tells Syd that they'll be extracted in about six hours. As the driving beat of Depeche Mode swoons across the soundtrack, Syd and Bucky do The Dance Of Flirtation. Syd's all, I'd love a fire in the fireplace. Bucky's all, keep yer pants on, Chiquita -- a fire would show up on Kasineau's thermal-seeking equipment. Then he wants to know what Syd was looking for in the database. Syd tells him a truncated version of the Spy Mommy sob story, and winds it all up by saying that she wants to let him in, but she doesn't feel comfortable doing that quite yet.