About the weird post above by coinxed: coins can be destroyed by not redeeming the entire coinbase, and also by sending an unspent output to (non-P2SH) script that always returns false. Some relevant info is discussed in this thread (e.g. post #164), and in footnote 9 in the paper (post #167) etc.
What happens if the N PoS "miners" aren't online? That seems quite likely very often.
The reason why you aren't worried that all the PoW miners will go offline is that they're rewarded for their work. Similarly, if stakeholders are rewarded, then we can expect some fraction of them to be online. In section 3.2.1 of the paper we describe how to incentivize a target participation level of the online stake.
BTW in case someone prefers to look at the presentation form, here are the slides that I presented in a couple of talks:
http://www.cs.technion.ac.il/~idddo/PoAslides.pdf