NEVER EVER COMPLETELY DISCHARGE A RECHARGABLE BATTERY.
Rechargables are secondary cells. They CAN reverse the polarity if allowed to go completely dead.
LiPo - LiPoly batteries are very sensitive to abuse. LiPo are not common. Lithium Ion are. Li-Ion are more forgiving. LiPo can catch fire if abused.
The only battery that has a "memory effect" is the old NiCd. NiCd cells would create cadium crystals and the crystals would fool the battery.