A surplus means that the quantity supplied exceeds the quantity demanded. The surplus exists only above the equilibrium. If the market is free, the surplus will tend to disappear as the price is lowered. The surplus will continue only if the market is not free; that is, a minimum price has been instituted by government. If the minimum price is below equilibrium, it is irrelevant and has no bearing on the market.
Prices of many agricultural commodities, such as milk for instance, are subject to government price support. This higher price encourages farmers to produce too much: this creates surpluses. For instance, in the 1980's, the government has been forced to make cheese from milk surplus and to distribute that cheese free to poor people.