Ceiling fan ground wire...?

I need to connect the green fan wire to the green ceiling wire or bare.... there is no green ceiling wire just a white and black. There is an actual hard wire that's tucked down... do I connect the green wire to it? And how, the green wire has a frayed end with actual wires, the ceiling wire is an actual single thick wire. How would I cap it off... would I just twist and leave it bare. Or can I just forget about the green wire and cap it off. I'm not using a remote or anything I've read that's what the green wire is for. I do see some screws in there but they just look like they are holding the box. I need help