POS and POW are completely separate and different systems. They do not depend on each other at all. They work separately and can compliment each other as 2 different methods to secure a block chain or they can each stand alone.
Also though by the sound of it they can separately and independently conduct their attacks?
If so then maybe for example a PoW attack can be accomplished and over and done with then a PoS block or series of blocks come along taking the success of the attack as valid accomplished fact and building upon it?
And maybe vice-versa also?
So that although they are two independent separate means of securing a chain they are also two separate and independent vulnerabilities whereby attacks can be performed?
-MarkM-