What should I do about this stray cat now?

Guys, there was a stray cat who came to our house 1 year ago. I fed him a little bit so after that he stays but he won't let us touch him or tame him. Whenever I eat he comes and meows so I give him little food. But few days ago my monther brought a live chicken and she wanted to pet it. The chicken got closed to us, whenever I woke up late in the morning she used to poke and wake us up. But one night while we were sleeping the cat eat that chicken and left her piece of leg.

After that incident my mother never let that cat enter the house although she never liked cats. But that still comes and sleeps inside our house. I chase him away everytime he comes and meows at me while I'm eating.

What are your opinion about it and why would a cat do it?
What should I do about this stray cat now?
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