1. A flash memory device comprising: a memory array including a plurality of blocks of memory cells; and a controller to perform a leakage-suppression process, the leakage-suppression process comprising: determining that a given block of memory cells includes one or more over-erased memory cells; upon said determination, performing a soft program operation to increase the threshold voltage of the over-erased memory cells in the given block; and writing status data in memory associated with the given block of memory cells after applying the soft program operation, the status data indicating that the given block does not contain over-erased memory cells.