Random Envelopes

So, apparently I misread that snake puzzle from last time, the intention was to get to a position where there is only one type of snake, rather than one where there are equal numbers of all snakes. The solution is basically the same, but the "brute force" method of applying AⁿB^mC^k is slightly less effective, since you must prove that you cannot reach any of 45-0-0, 0-45-0, 0-0-45, so hitting on the mod 3 solution is more needed.

Anyway, I found a new puzzle on the xkcd forums, I thought it was sort of cool:

Alice and Bob are having a conversation that you are overhearing. Alice has a collection of N envelopes and says to Bob, "for each of these envelopes, it contains either a dollar coin or nothing, I chose to fill the envelopes at random, what is the expected value of the contents of a random envelope?"

Bob responds, "It depends on the method you used to decide to fill the envelopes. You could have flipped a coin for each one, filling it if you got heads and not if you got tails, in that case the expected value of an envelope is $1/2."

Alice decides to tell Bob the method she used to fill the envelopes, she whispers it to him. "I see," Bob replies, "I will purchase a random envelope from you for the expected monetary value, then." Alice agrees, Bob hands her some money and selects an envelope. Bob finds that the envelope does contain a coin and pockets it.

Alice takes the now-empty envelope from Bob and shuffles it back in with the other envelopes. Alice says to Bob, "what is the expected value of a random envelope now?" To which Bob replies, "it is the same as before my purchase."

What is a possible value for N and random method that Alice could have used to make this scenario possible?

When I first read this puzzle, I was certain it was impossible. There is no way that Bob could have taken a coin away and not changed the expected value of a random envelope. However I was missing something. Obviously not something stupid like "Bob can see which envelope he opened earlier because it is now torn" or something like that, that would hardly make an interesting puzzle. There is a well-defined method that Alice can use to make it so that after Bob finds and removes a coin the expected value of a random envelope has not changed.

There are actually many possible solutions, so when I do post the solution next time it will by no means be a complete listing of all possibilities (there are far too many), try to see if you can come up with at least one possible solution though.