You define a consensus rule in NewStakeChain that it must include within it a valid block for OldChain that contains no transactions, or otherwise causes damage to the network by making it unusable such as a reorganization proof. Once the OldChain network has been destroyed by the new one, the consensus rule can be relaxed and there no longer needs to be POW completed by anybody.
This specific example works and is economically rational because miners could make a PoW block and get its reward, or they could make the no transaction attack block and get its reward, plus the reward on NewStakeChain for submitting the proof.