Unusual wiring in ceiling box for installing light
Do you have any wall switches that either don't seem to do anything or that control an outlet? If so, check with a non-contact tester to see if the switches have any effect on either or both of the wires. One possibility is that the "free" wire is a switched hot and the "loop" wire is neutral. If so, then you should be able to split the neutral (cut, wire nut the two ends + pigtail to lighting fixture) and use that together with the switched hot.

Thinking about this a bit more, a neutral passing through (but not split) is common in a switch box (where switches that don't need a neutral will have the wire present but not connected to anything, just passing through to the fixture) but I am not quite sure how/why that would be the case in a ceiling box like this. Each switched fixture should have a separate neutral going back to the main panel, together with the switched hot back to the switch and then with the hot back to the panel. So while I can see a way the neutral might loop through, I'm not sure it is correct - so you really need to determine if it is a neutral - and the correct neutral (though why there would be a different neutral in the same location is beyond me) - or not.

If you can't find a switch that has any effect on any of the wires in the ceiling box then forget about trying to do anything with it, as the wires are likely for something else - e.g., central smoke/fire alarm.

HOWEVER, before cutting any wires or installing anything:


Determine the active breaker for the circuit, shut it off and make sure there is no voltage on the wires
If you are renting, check your lease for what you can/cannot do and/or talk to your landlord. Even if you think it is just an improvement, there may be non-obvious reasons why this is not a good idea or simply not permitted. The landlord may (quite legitimately) only permit any wiring changes to be done by a licensed electrician. Or the landlord may not care at all as long as none of the other apartments are affected.