Minnflyer is right.

If you turn off the switch to the Rx, the servos no longer have power. Without power the Rx will not respond to inputs from the Tx and the servos cannot move (because the servos don't have power either). Unless the switch is faulty and would allow for the receiver to still have power.

My suggestion would be to check the switch or replace it. If the switch is OK, could someone have accidentally turned on a Tx on the same channel???