When an active chain of command blocks is destroyed and then replaced with an identical, inactive chain, the game becomes confused and continues executing the commands. Similarly, if chain command blocks set to "needs redstone" are depowered while executing their commands and soon repowered, they'll simply pick up where they left off.

The exact circumstances under which I discovered this glitch: I had a long chain of command blocks set to 1200 tick delays, forming a timer. The only issue is, I needed to be able to stop that timer under certain circumstances. So I tried setting them to "needs redstone" and depowering them; they simply resumed where they left off when I powered them again after 10 ticks. I tried completely deleting the command chain and replacing it with a depowered identical copy after 20 ticks; it merely picked up where the old chain left off.