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So let me get this straight.... Kate finally gets the signature that her employers are so desperate to have to complete that all important buyout, and she doesn't even bother to send it to them on that helicopter?
I understand her decision to basically quit her job and go adventuring, but it seems rather irresponsible and disloyal, even aholish, to not send the signed contract to her company.
Kate was worried about an old man takin' off on a train to god knows where with no one to look after him but an automaton, so at that point the contract was the last thing on her mind.
Also, had she wasted any time worring about getting the contract delivered and whatnot, and she wouldn't have managed to get on that train, and you know what that would mean, right ? No Syberia II ;)
Without having played the second one yet, I'm imagining that she mailed it over whenever they got to a place with a post office.