The fact that the "sinkers" are such an integral part of the game, means that if you run out you either have to pay for more, or keep starting a new game until you get lucky enough to get a bonus. Also if you are out of sinkers and have no moves left the game does not end, it brings up the purchase screen right away. The game should automatically end once there are no moves left and only after give you the option to buy more sinkers or start a new game. Start a new game with a replenished amount of sinkers--1 or 2-- and allow to carry a larger amount by purchasing.
HankScorpio13 about Sinkers, v1.0