Theories...
Xigbar's eye-patch
#1- Trying to figure out how to use his weapon
Xigbar is sitting at the foot of his bed.
"Okay, so I'm a 'Nobody', huh? So that means I'm now able to summon up a weapon that was given to me, then." So he summons up his new weapon. "An arrow gun, then, huh? Cool." Xigbar looks at the gun from different angles. "So, then, I load it up like this, I guess. So, now, how exactly am I supposed to shoot this thi-" he accidentally pulls the trigger as it's pointing at his eye.
"!"
Thus explaining the eye-patch.
(Me)- Ehehehehe... he's so much fun to joke around with... but this is one of my many theories... don't worry, I'll have some more interesting ones...