Does patrolling with 0 unrest kill population too?

[Endoperez]

If there is unrest in province, patrolling forces look out for the troublemakers and kill them, reducing unrest. Population is lowered by a certain number (5?) for every point of unrest removed.

The question in this thread was whether patrolling reduces unrest if there is no unrest present. It doesn't, and because of this you have no reason not to patrol with your armies when they are in your fortress: if there is a surprise attack, your forces will catch the attackers.