The Flash Lite version of the SharedObject class offers persistent data storage on the device. It allows SWF files to save data to the device when it is closed and load that data from the device when it is played again. For more information, see the Flash Lite 2.0 documentation.
You can use the Adobe Device Central Persistent Storage panel to determine how full storage is on a device. The Used/Free indicator is a per-device value, so if multiple SWF files write to the persistent storage, the value is the sum of all their data.