Two different things have been discussed leading to some confusion.
1) What the OP was asking about is whether ESP should completely stall the engine when it acts. According to him it did somtimes and sometimes not. Answer is that we think it should not and noone else has reported this problem.
I don't know if the fuel is completely cut or just limited when ESP intervenes but if it's cut completely (or to an idle supply) I guess it's possible if directional control (according to the ESP sensors) is not regained before the engine revs fall below the limit where it can continue to run, it might just stall in the same way it will if you allow the revs to fall too low while in gear and under load. In other words if ESP never gets the car "straightened out" so you can continue on it might ultimately stall the engine. Assuming manual.
2) The second thing that was discussed is the engine power also being cut whenever the brake and accellerator were applied together. While some of the same sensors and logic may be involved this is a separate thing and probably just a sensible safety measure to allow the brake to stop the car in any circumstance where the throttle may be stuck or pressed by the driver along with the brake which for most situations is illogical.
3) There is one other thing that has been discussed before and that is in essense a combination of these two things by inadvertently invoking an ESP "event" by juditious use of left foot braking to provoke a controlled rear-end slide (oversteer) while negotiating a corner at speed. This manoevre cuts the power to the engine just when you most wanted it! Whether the power is cut by sensing situation (1) or (2) above, I don't know. Probably just a standard ESP intervention (1) unless the brake is applied sufficiently long to invoke (2). The handbake could be used similarly.
As I said before, I have no knowledge of how the logic works and I'm just guessing.