How does a flight control computer deal with control surface disengagement?
Well the A320 and A340 have 2 actuators per deflection surface (in case of elevator or aileron, spoilers do not have 2 actuators per 1 surface).

If one of these actuators fail, as in they have no pressure supplied to them by either hydraulic power systems (Blue,Green,Yellow) the other actuator which is supplied by a different pressure supply system (to avoid a single point failure) will take control of the of the surface. The flight control computer would continue working under normal law given that the other 2 Primary flight computers (PFC) are working properly. However, if the secondary flight computers(SFC) take control (after at least 2 failed PFCs), the aircraft would lose the ability of flight with normal law and thus direct law would be activated. 

A disconnection between LVDT and a deflection surface would cause a disruption of the feedback towards the PFC. The PFC will notice that it is sending signals but receiving no change in feedback and will consider itself out of order. This would mean the respective PFC will render itself in a passive state and pass control to the other PFC connected to its own actuator. Depending on whether a PFC or an SFC in control, you would have either normal (at least PFCs intact) or direct law (the 2 SFCs are in command)

A Mechanical backup is available in the form THS(Trimmable Horizontal Stabilizer) which is activated by the trim wheel and the rudder which is available through the pedals for the A320 and A340.