Flooding caused by tropical cyclones depends on the speed at which the storm is moving. Heavy, torrential rains can occur hundreds of miles away from the center of the storm, and impact areas even if it does not make landfall. Even after the winds have subsided, the flooding potential from storms can remain for several days. Nearly 60% of the deaths due to hurricane flooding have been from drownings related to inland heavy rain events.
Source: Rainfall for Tropical Storm Debby | NOAA