Law 68D2bii - Play continues after the claim
A defender claims and faces his hand (68C).
They all agree to play on (68D2bii).
Per 68D2bii, the information about his partner's faced hand is not UI to the non-claiming defender (Law 16 does not apply), and so can properely be used.
Suppose the defenders gain through the information available.
Is there restitution, or is this a case of "Cave Declarer"?

Comments
"Laws 16 and 50 do not apply, and the score subsequently obtained shall stand"
Of course information about the defender's hand is AI for declarer as well.
Does law 50 apply to all cards or just the cards exposed by the claimer. In other words, if their partner exposes their hand are all those cards now penalty cards if everyone decides to play on?
(There is also a slight problem in that a defender cannot claim if the action involves their partner having to make a choice of 'normal' plays - the TD must assume their partner will go wrong if is a possible decision),
They can still claim I think, it's just that both hands having been exposed make declarer playing on rather than asking for an adjudication even less advisable. Actually, on checking Law 50, the procedure for a claim only states that the player making the claim shows their cards.
So the partner exposing their cards is in a technical sense an irregularity. Legally it's a bit tangled. Law 68B2 tells us that if they immediately object to partner's claim then no claim has occured but Law 16C on unauthorised information applies. Assuming this doesn't apply then I would probably consider that doubt as to the claim has occured and we shouldn't play on. Which is a bit of a stretch in terms of the laws but seems a pragmatic approach.