leftover, remain, balance
殘 centers on what is left behind after something is taken away or finished: a leftover, a remainder, or a balance. It can also imply something that persists or remains.
殘 combines 歹 (death, harm) with 戔, which likely contributes the sound and the idea of smallness or diminishing. Together they suggest something reduced or left over after harm or loss. The modern Japanese simplified form is 残.
The left side 歹 suggests death or damage, and the right side 戔 looks like two small spears. Imagine after a battle, only broken spears and remnants remain—those are the leftovers.
For ザン, picture a Zen monk calmly sweeping up the last leftover grains of rice after a meal: Zen -> ザン, and the monk ensures nothing remains.