I wonder if the price of 1 CPY (CEN) can fall below the smallest part of bitcoin - 1 Satoshi?

It is already close.

1 CPY = 2 CEN, and CPY price is pretty far from 1 Satoshi...
Check CMC
COPYTRACK (CPY) CPY/USD = 0.010628 USD
CPY/BTC = 0.00000097 BTC
CPY/ETH = 0.00003665 ETH