Thick copper wire in the wall? Outside the box? An individual single-strand wire without insulation? Thick? Larger than the conductors that were connected to the fixture?

If the 'thick copper wire that was curled up in the wall' is part of the cable that the old fixture was wired to, then yes, connect it to the bare copper wire from the new fixture. Not grounding the fixture leaves you at some risk of an electrical shock if the 'right' type of failure occurs.

To bus driver/Randy: yes the thick copper, single stranded, uninsulated wireis in the wall and outside of the box. It was not attached to the old fixture at all. Since it wasnt attached to the last fixture, should I leave it curled up in the wall and attach the thin copper wire to the green ground screw?

The copper wire in the wall is attached to/comes from what/where? Does it come out from the same cable as the insulated wires that are in the box and to which the fixture was attached? Does the wire come into the box and then out again? For the cable supplying power to the box, does the cable outer sheathing enter the box at all?
For the more knowledgeable on this forum, this wire outside the box is so unusual that I think it unwise to just assume that it is the equipment grounding conductor. It takes extra effort to have that wire outside the box. Who knows what other "creativity" was exercised by the installer? Who knows what that installer did with the other end of the wire?

Unless you can find the other end of the wire do not use it for ANYTHING.

In-other-words a picture is worth a thousand questions. Please post an image.