After listening catwoman tapes from arkham city especially the number 5, i notice that strange actually helped catwoman steal his own vault it was him who give the tip about two face safe that she stole at the beginning and inside was the fucking blueprint of the tyger vault.

Hugo goals are to destroy batman, and purge all villains in protocol 10, but why would he do this?

-let her steal his cash and leave to arkham city help him to kill batman in protocol 10 since he is removing one of his allies from the board, but he spared a villain doing that.

-maybe he thought that she would return to arkham city after he started protocol 10(note that there was no way he could know that she would heist him on the middle of protocol 10) because batman would be in danger and may need her help, but still the oposite happens he places a villain back into his cauldron but helps batman, maybe he knew that she had the skills needed to escape arkham city and used this to "confine" her.

-or he just wanted her to make chaos in arkham city and didn't give a fuck about her decision, he already sponsored joker and penguin with guns so they can kill themselves and give him reason to do the protocol 10, this also explain why he told two face that catwoman was preparing to steal him, but still he could have manipulated her in a way that he would not be robbed and he could not predict that two face would have catched the coin(he tested two face to see if he wanted to treat his mental illness or remain a villain).