How to handle late game tile drawing in Tsuro
The rules in my copy and on the official site are quite clear:


  If the active player has the dragon tile, he or she places it at the bottom of the draw pile and draws a tile from the top. If the active player does not have the dragon tile, he or she draws a tile from the top of the draw pile.
  
  Starting with the active player and moving
  clockwise, each player with fewer than three path
  tiles draws a tile, continuing around the board
  until all players have three path tiles or the draw
  pile is empty.
  
  When new tiles become available later in
  the game, the first player to draw a tile will
  be the player with the Dragon tile instead
  of the active player. That player sets aside
  the Dragon tile when drawing a path tile.


That said, they are quite wordy. So let me rephrase them:

Let's say the draw pile is empty and tiles are added to it because one or more players were eliminated. If someone has the Dragon Tile, take the Dragon Tile from whoever has it and place it at the bottom of the deck. Deal one tile to them, one to tile to the player next to them, one tile to the player next to that player, and so on until everyone has three tiles or someone draws the Dragon Tile.