If being part of "The DAO" is similar to being a shareholder in a company, how is the passive DAO Token holder affected by decisions made by the active participants. If for example, the Slock.it project is somehow supported by The DAO, but the passive token holder didn't vote on the project, will the passive token holder still reap any benefit from the project which was part of an overall DAO initiative?
The DAO gets a lot of comparisons to shareholders, but mostly in this sense: Your shares give you the right to vote and the right to collect "dividends" (reward tokens) and so it's in your best interest to vote, but you don't have to vote to collect your dividends.
When there is a proposal to vote on, you call the "vote" function from your wallet with the proposal ID and whether you are voting for or against it. The vote is boolean - meaning it's yes or no and that's it.
You don't have to vote on a proposal to get any rewards from it. If you hold tokens when the proposal is passed and executed, you are invested in that proposal proportional to your share of the total existing tokens.
Your tokens are yours forever, unless you burn them in a split or trade them on an exchange. You're not really "using" them to vote, the contract is just checking your balance and using that to assign a weight to your vote.
As long as you hold your tokens, you are investing in everything the DAO invests in (and rejecting every proposal the DAO rejects) whether you vote or not.