If you were moving and put the bike in too high a gear or failed to pull in the clutch in time as slowing down, the bike would buck and sputter very noticeably before it shut down and it would only shut down if you were in say 3rd gear at 5 mph and upon discovering this, tried to accelerate rather than pull in the clutch to down shift or just allowed the bike to come nearly to a stop and didn't use the clutch. It would happen going up the hill much more easily. Going down hill as was mentioned, the rpms will increase and take the strain off the engine even if you are in too high a gear. If you didn't try to accelerate, you could go down most hills in 6th gear and it shouldn't put a strain on the engine even if you were going only 25 mph.
Just engine braking shouldn't shut down the bike so you must be braking too then releasing the clutch in too high a gear. I mean if the bike is idling OK when stopped at traffic lights and you shouldn't need to open the throttle at all while idling, then if it dies when going downhill, it must be you are in too high a gear for the speed and that is likely to happen only if you are using your brakes. It wouldn't just die though. It would jerk and sputter, buck, rattle, and maybe even backfire with all the strain on the engine before it died. Going down hill and releasing the clutch is how you can start a bike with a dead battery usually in second gear. It shouldn't be killing the bike.