The other day riding home I noticed the inner lip of the sprocket separated from the sprocket I've seen a few others on here break them. But I was curious if anyone's attempted to fix or repair since they just appear to be pressed on?

 

They are pressed and swaged. I had one come lose but replaced it, however it may be possible to do a repair, with the right skills.

 

If the loose ring has not been damaged and the mounting recess is OK, it can be remounted and swaged. I have done this to one before.
Be careful when putting the lip back on so as to not spring it out of round or bend it.
A cold chisel or center punch will swage the pulley material into the rim to retain it. Do it in many places all around the pulley.