Damage, Injury, Harm
You slip off the roof, your life flashes before your eyes, and you smash your mouth on the ground causing some serious damage. Oof, this is a really bad injury, you fell all the way off the roof and onto your mouth.
Imagine that moment as you fall off the roof. In slow motion you can see the roof moving away, you see yourself as a little kid, a teen, an adult, then BAM you've injured your mouth. Ow ow ow!
がい
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As you try to assess the damage, you hear someone shout, "Guy (がい), hey, you okay, guy?" They run up to you, but your mouth is too damaged, you can't respond. "Okay guy, I'm gonna call you Guy now. Let's get you to the hospital."
No matter how much you try to wave your hands and gesture, they keep calling you Guy. It's really annoying, actually, because you aren't a guy and you aren't Guy either. But your mouth is too damaged for you to tell him.