Neon Tetra And A Eye Missing Eye

Hi. Two months ago i got 6 neon tetras in my 10G tank (cycled, proper temperature and parameters, a sponge filter, with daily +-5% water change, gravel vac once every 2 weeks).
It also houses a betta who is cool and does not bother to waste time on tetras. He is probably just old.
Last week one of my tetra went missing. And couple of days ago the youngest/ smallest tetra is missing his left eye.

Has it happened with any one else? I feel that the bigger neons are culprit in it as the betta- even now will just swim alongside the half blind tetra but never goes after him.
Also i fast all my fish once every week. Is it possible that they go hungry and went cannible?

 

Unused to have neons and a betta with no problems swam together or so I thought untill one day I came in to find a neon hanging out of its mouth and I lost a few this was a year or do ago I have since lost the betta but he was fine with the neons 99% of the time but did kill a few off