NiCad cells have memory effect
NiMH cells have memory effect but to a lesser extent. They're better than NiCad in almost every way.
The K800 is definitely NiMH, and they're not user-replaceable (which means they're probably just soldered together)
Lithium cells are different, they have no memory effect but they don't like being over-drained, nor overcharged. Most Lithium power circuits prevent trickle-charging from overcharging the batteries, but the ideal state for the optimum 300-400 cycles of lithium is to never go outside of the 50-80% charged state. If a lithium cell (nominally 3.7V) drops to 2.2V it's destroyed and will likely explode if prolonged attempts to charge it are made. Most devices consider the battery at 0% when they reach ~2.5V and only last for around 120-150 cycles if each cycle is a full cycle from 4.1V to 2.5V.
It's all about managing the oxidation in the cell. You get 10-15% more capacity per charge if you're willing to sacrifice the battery cycle endurance by lowering the cutoff voltage, but the sweet spot for longest lifespan is probably 3.6V which will usually show as 10-15% remaining (depending on temperature and discharge rate). The precipitous drop in voltage is because oxidation changes the internal chemistry of the battery in that depleted state, and the voltage is specific to the chemistry.