A funny situation.
Let's get some guidelines.
a) For turbine engines, sfc (specific fuel consumption : kg of fuel to produce a unit of thrust or power) increases as the rating of the engine is reduced.
b) endurance mission require least fuel flow per unit of power used.
c) Typical Loiter missions need low power (30% of max power on the aircarft?)
From this point of view, is it practical (!) to use only one engine in a twin engine turboprop aircraft. Let's say 400 HP is required for the mission to be flown which may mean 30%-40% rating operation. This puts the engines in high fuel consumption operation.
On the other hand, if one engine is kept idle, and the other used at a higher rating (70% ?) to produce 400HP and improving the sfc, a significant gain can be made on the fuel flow rate. This should increase the endurance time.
Of course, rudder and ailerons need to be deflected to take care of the adverse yawing moment created due to asymmetric thrust. They will produce some drag which will reduce the fule flow rate gains to some extent.
Your comments on this type of operation are most welcome !