Another possibility is that one (or more) of the 3 installs spyware on the other collaborators before the generation (or at least before the subsequent destruct

Another possibility is that one (or more) of the 3 installs spyware on the other collaborators before the generation (or at least before the subsequent destruction) of the private keys. Then the attacker waits a while and then combines all the captured keys to produce the combined private key and claim/spend the mother lode.