You would survive until you draw a card (such as if somebody cast a Blue Sun's Zenith targeting you). You would not die during your Beginning phase because you wouldn't be drawing any cards during it.
July 23, 2014 11:35 p.m.
Sure there are plenty of rules that confirm this. They can even be found by going here and reading about the ways you lose the game (by the way you just lost The Game). As a matter of fact most questions posted here can be answered by going there and hitting ctrl+f. If you don't take the time to do so why should anyone else take the time to go find rule 104.3 and quote it in its entirety so that you can see all of the ways to lose and see that they are:
104.3. There are several ways to lose the game.
104.3a A player can concede the game at any time. A player who concedes leaves the game immediately. He or she loses the game.
104.3b If a players life total is 0 or less, he or she loses the game the next time a player would receive priority. (This is a state-based action. See rule 704.)
104.3c If a player is required to draw more cards than are left in his or her library, he or she draws the remaining cards, and then loses the game the next time a player would receive priority. (This is a state-based action. See rule 704.)
104.3d If a player has ten or more poison counters, he or she loses the game the next time a player would receive priority. (This is a state-based action. See rule 704.)
104.3e An effect may state that a player loses the game.
104.3f If a player would both win and lose the game simultaneously, he or she loses the game.
104.3g In a multiplayer game between teams, a team loses the game if all players on that team have lost the game.
104.3h In a multiplayer game, an effect that states that a player wins the game instead causes all of that players opponents to lose the game. (This may not cause the game to end if the limited range of influence option is being used; see rule 801.)
104.3i In an Emperor game, a team loses the game if its emperor loses the game. (See rule 809.5.)
104.3j In a Commander game, a player thats been dealt 21 or more combat damage by the same commander over the course of the game loses the game. (This is a state-based action. See rule 704. Also see rule 903.14.)
104.3k In a tournament, a player may lose the game as a result of a penalty given by a judge. See rule 100.6
And that no where in there does it mention starting your turn with an empty library, only attempting to draw from an empty library.
July 24, 2014 1:12 a.m.
In case this isn't clear enough, here's how this turn would play out.
Trigger put on stack, priority passes, trigger resolves.
Searching empty library. Fails to find. Shuffles empty library.
Main phase one.
Turn carries on as normal.
July 24, 2014 2:19 a.m.
So that means i can never die from not having a library b/c of that trigger from Elfhame Sanctuary . I think i have enough info to justify my survival for the next time I would have an empty library. Thanks!
July 24, 2014 2:23 a.m.
Yes. You only die if you draw a card without a library. Elfhame Sanctuary prevents the first draw each turn. If you draw a card for ANY other reason, you still die.