I removed a fluorescent light fixture from kitchen but I'm not sure the work box will support a real light fixture. The work box is round and plastic. The fluorescent light wasn't even held up by the work box, it was attached directly to the ceiling.
I've installed light fixtures before to metal work boxes and its usually replacing another light fixture attached to the work box, so I know they can handle it. For this one I'm just not sure.
Here are pictures of the work box in question:
Best Answer
These type of boxes usually have 1 or 2 screws going through the bottom into a steel bar that spans between ceiling joists.
I think you are correct that this box is not properly supported.
If you have access from above, you can put a support (2x lumber) across to each joist and then screw through the box into the support.
Options from below only would involve removing the existing box and using one of several replacement boxes. Removing the existing box will involve turning off the power and prying the electrical cable loose from its strain relief. From the looks of the box, it should pull down. Fixture weight will determine which one to use.
The heaviest duty box is one rated for ceiling fans. It uses expandable threaded supports that wedge against the joists side to side. This box would be rated up to 50lbs.
An old work round plastic box has three retractable wings that clamp the box against the drywall. This box is suitable for lighter fixtures, perhaps up to 10lbs. It is very dependant on intact and unbroken drywall for best performance.