If the government cuts the subsidy provided to tobacco farmers, the farmers would have to compensate for the decrease in their revenues earned by increasing the cost of tobacco that they sell to the companies manufacturing cigarettes. As tobacco is a primary raw material used in making cigarettes and does not have any substitutes, the cigarette manufacturers would have to increase the cost of cigarettes. The price of cigarettes can be increased without a substantial decrease in the quantity that consumers buy as the price elasticity of demand in the case of cigarettes is quite low.
As more people quit smoking to avoid having to face its harmful impact on health the number of buyers decreases. This decreases the demand for cigarettes and leads to a drop in their prices.