I don't have specific knowledge of the T7 either, but perhaps this would happen:
Following one engine shutdown, the autopilot will maintain heading and altitude. The autothrust will increase thrust on the remaining engine as required to maintain airspeed. If max. climb/cruise thrust is not sufficient to maintain speed, the airplane will slow down, still maintaining altitude. The autopilot will disconnect either when the speed becomes too low, or at the second engine shutdown, if that occurs earlier. With two engines shut down and autopilot off, the airplane will descend at approximately constant airspeed, probably fluctuating around the trimmed speed in a phugoid fashion.
The report says "spiral descent", but the more sensation-hungry posters immediately translate that to "spiral dive".
Gysbreght,
(2nd hand info...)
The B777 simulation results from the last month show that the one engine out case is handled gracefully - TAC (Thrust Asymmetry Control) will keep the plane flying straight. At first airspeed will be sacrificed due to single engine thrust limits. Then, altitude will be sacrificed to maintain airspeed. Eventually, flight will stabilize at an altitude and airspeed combination appropriate for the single engine case. (There are specific max engine limits for single engine operation that 'can' be different from the limits for 2 engine opration.)
An article I found very informative on TAC (beyond reding the manual...)
Thrust Asymmetry Compensation
Things get uglier when the 2nd engine cuts out...
1) TAC will (would?) drop out when it detects that both engines are out.
2) When the engines stop supplying AC power and hydraulic pressure, the hydraulic flight controls (including the TAC-adjusted rudder) will remain locked in place.
3) The Autopilot will drop out (disengage) with the total loss of AC power.
>> This creates a race condition in which the exact sequence of events will determine the flight control settings locked in after power is lost.
The suggestion has been made that the Autopilot would drop out first, with the rudder trip from TAC still fully applied. This would lead to an unfavorable condition while power is out. And, when power returns, the autopilot remains disengaged, so these flight control positions will be maintained.
-- This is what leads to the expectation of a very short glide period. The the plane will begin turning right at 2nd engine flame out, and continue that turn even when power is restored from the APC and/or RAT.
This is most likely the 'spiral decent' mentioned in the June 26th ATSB report.