There's no aerodynamic reason they shouldn't be able to do that. Fighter pilots and aerobatic pilots have been performing maneuvers that involve deliberately stalling the wing since the very early days of flight. But perhaps a description of a very simple form of stalled-wing maneuvering will help you visualize how it works.

The first thing we have to do is correct the commonly held misunderstanding that a stalled with "loses lift." That's a very poor way to describe what happens because a stalled wing still produces lift proportional to the square of airspeed, it just does it with more drag and at a higher AOA. If you doubt that, consider that a paper airplane wing is essentially stalled all the time. A better way to think of it is that stalling the wing results in a sudden shift to a lower lift to drag ratio. The wing can still produce 1 g of lift (or however much lift you want), but at much higher drag than the same wing when it is not stalled, and at higher airspeed.

Probably the easiest stalled-wing maneuver to understand is the technique used by bush pilots to minimize damage in an off-field forced landing. The pilot flies the airplane into a stall and holds it there, with aft stick, while maintaining stability with the rudder (not with the ailerons). This results in a glide with a much steeper than normal descent angle but with a low vertical speed, because the airspeed is low. (Glide angle is inversely proportional to L/D.) The pilot can then fly the airplane to a smaller clear area on the ground than they could hit with a normal glide, because of the steeper glide path. Damage on impact is minimal because of the low airspeed and low vertical speed. In fact, with a good STOL airplane, very short landings can be made on a normal runway with no damage at all. I have done this may times in a Druine Turbi, stopping in well under 200 ft from the runway threshold.

The trick with a fighter jet is to have enough control authority to usefully maneuver the jet in yaw and roll with the wing stalled without having surfaces so large that they compromise un-stalled performance. It's also helpful to have loads of low speed thrust so you don't lose more energy during that maneuver than necessary.