I am changing light fixtures and noticed that the end of the ground wire is not accessible from inside the electrical box. The ground wire simply passes through the box. I've gently tugged on the ground and it seems secured to something. There is only one 14-2 cable coming into the box and only the ground wire leaving it.
It looks like that electrical box has a mud ring installed on it. The box itself is clearly of a molded type construction such as a phenolic or bakelite or plastic material. If the mud ring is made of metal it is possible that the original installer wrapped that ground wire around the mud plate mounting screw in order to ground the ring. This could be the reason that you cannot pull the end of the wire free.
It is unlikely that the ground wire exits the box completely and travels off to some other destination. If that is the case you may be able to reach inside the box and cut the wire in a manner to maximize its length and then simply attach the light fixture ground to the end of that wire.
An alternative, while not optimum would be to bend the ground wire back on itself so that it comes to a double width point. Then use a green wire nut to attach a bare solid copper wire pigtail. Then the pigtail becomes available for connecting to the light fixture ground.
Tug the wire with a little more confidence -- it's probably just pinched somehow.
Failing that, if you want to leave the end captive as-is, then clean off the paint etc from the wire, cut it, and use a push-in or twist wire connector to re-join the two parts and provide a place for connecting the additional conductor for the light fixture.