Yes, some people can pass out from stress. When you are stressed-out, have anxiety, see danger, or have sight of injury, some people can activate the parasympathetic nervous system, which drastically decreases your blood pressure by slowing down your heart rate and dilating your blood vessels. Then the blood rushes out from your brain due to the decrease in blood pressure, and then you faint.
The other way you can pass out from stress is that stress and anxiety activates the sympathetic nervous system and also triggers the release of adrenaline, in a reflex called the fight or flight response. This may cause an increase in your breathing, but you may breathe so fast and so shallow that you hyperventilate. When you hyperventilate, you are not getting enough oxygen to your lungs, as you are breathing too fast and hence breathing shallow breaths. The oxygen reaching your brain drops drastically, then you faint.