Edit for justification:
This question is different from If the EPU (Emergency Power Unit) on a modern fighter jet fails, will the aircraft drop out of the sky? for the following reasons:
The question in If the EPU (Emergency Power Unit) on a modern fighter jet fails, will the aircraft drop out of the sky? asks if an aircraft drops out of the sky if the EPU (Emergency Power Unit) fails, for a generic aircraft. The accepted answer only briefly touches on the F-16, and certainly not in a way to answer this question. This question is specifically about an aircraft with RSS (Relaxed Static Stability), and how this relates to loss of hydraulics and power.
The F-16 has Relaxed Static Stability (RSS) to enable a high degree of maneuverability.
This causes the aircraft to be inherently unstable and RSS is corrected for by the on-board computer in real time, as part of the fly-by-wire system.
In the event of loss of hydraulic power, the ailerons cannot be operated, the on-board computer/avionics will also fail, if there is no power. The EPU (Emergency Power Unit) will re-establish hydraulic and electrical power, but this doesn't happen instantaneously. It takes some seconds.
During this critical window, what allows the F-16 to remain in stable flight in the context of RSS?
Reading this PDF it seems that the F-16 can be unresponsive to pilot input, yet remain in stable flight.
My question is, how is this achieved? How is it possible?
My own reasoning:
Either the F-16 is not as inherently unstable as I'm given the impression it is, or, there is enough hydraulic power and electrical power left in the interim between power from main hydraulics to switching to the EPU to allow the fly-by-wire system to keep the aircraft stable.