Pretty much what it says on the tin--when you're drawing, say, 5 flood cards and there are 4 tiles left in the game, are you supposed to keep shuffling and re-drawing one of those 4, thus automatically sinking one tile per turn?
Yes. From the rule book page 8.
When the Flood Draw Pile Runs Out
If the Flood draw pile ever runs out, immediately shuffle the Flood discard pile and stack the cards face down to form a new Flood draw pile. If this happens in the middle of a turn, continue drawing Flood cards as necessary from the new pile.