I have a 99 deville that the engine dies at various times, ie within 1/4 mile when started (fALL), 40 miles after starting coasting down a twisty hill (WINTER), 2 miles after starting (SPRING), running on a flat road for 7 miles (SUMMER),etc. It has happened all times of the year in all conditions. No explanatory code is resident, fuel pump checked and working, fuel filter changed, air filter changed, fuel additives for injectors added. The vehicle usually wil start in 2 trys with a light pedal applied. Still happens and can’t find out why. this can be very dangerous as I was trying to corner down the twisty hill with no power steering.
How was the fuel pump checked? It could be working but the pressure regulator failing. Or pressure simply insufficient. Or the fuel filter could simply be plugged.
There are a few controls to check but they are all controlled from a central device. Maybe you should have that thing changed. No codes or nonsense codes points to the computer. It may be something else, but the something else is also costly to repair. It may be time for some guesswork. Throttle positioner may be gone. In the old days, 1985, you could adjust it all the way out so the idle wouldn’t fall too low, but Nobody recommended it then and only I would mention it now. I wouldn’t recommend it, but I talk a lot.