Surface deflection if loss of hydraulics on combat jet
Most of the ones that we measured without hydraulic pressure would just sit there. Moving the stick is possible within the servo valve deadband, but the surface does not move whatsoever, just stays in the last known position.

Hydraulically powered fighter jet surfaces are powered fully redundantly, by separate actuators and separate hydraulic systems. If pressure fails in system 1, opening the servo valve (by moving the stick) just connects pressure to return and its actuator becomes a passive damper that otherwise does not hinder the functionality of the remaining one. Yes the inputs to both servo valves are linked.

Most hydraulic power systems for fighter jets are irreversible, meaning the aerodynamic hinge moment cannot move the stick. But if the hinge moment becomes larger than the total force of the active actuators, the surface cannot be deflected anymore. 

Info on military jets don't seem to be not publicly available. I could find this hydraulic schematic for a G450 elevator:

 

This set-up allows manual reversion: when all hydraulics are off the pilot can manually deflect the elevator, at higher forces than with hydraulics functioning. Note that the pink colour denotes "Hydraulic Lock". It means that when the servo valve is closed, back driving the actuator is not possible due to trying to compress the hydraulic fluid.

Over (a very long) time, gravity may slowly push the hydraulic fluid back through the circuit when unpowered. When all oil in the circuit has seeped back into the reservoir.