In a perfect world, with perfect electronics, there would be no need for a grounding conductor. It's there to deal with imperfections. The most likely case for a ground fault in this installation would be if the black conductor lost some insulation and shorted itself against the frame of the fan. In such a situation, the casing could become electrified, and a grounded person, touching the fan body could receive a shock.
If it were properly grounded, you'd get a short circuit to the ground wire, and the breaker would trip.
However, the fan is mounted to the ceiling, and the possibility of someone touching it is low. (Unlike, for example, the frame of a fridge or stove, where human contact is part of normal operation.)
So, Is it safe? Quite likely. For added safety, turn the wall switch off when changing bulbs. Is it to code? No. -- Unless, as others have suggested in comments, the mounting box is grounded on the other side.
You can however, locate the breaker, and replace it with a Ground Fault Interrupt breaker, which would trip should a ground fault occur. This isn't something you should do yourself unless you have experience working in the panel.
Another possibility, if your switch happens to be chained off of an outlet, which is quite possible, depending on the routing of the wiring on that circuit, is to replace the outlet with a GFCI outlet, and wire the switch to the load side of it.
It sounds like whoever installed it, used the neutral as a hot and the ground as a neutral. Likely they wanted to control the fan and light separately, but only had two conductor cable between the switch and fixture.
If you're installing a remote, you'll only need the two conductors.
Without seeing what you have, this is what you might have to do.
- Disconnect the white wire from the switch, and connect it to the grounded (neutral) conductor in the switch box.
- Connect the bare grounding conductors in the switch box togther, making sure to disconnect any bare grounding wires that are attached to white grounding conductors.
- Follow the instructions to install the new fan and remote.
- in the ceiling box, connect white to white, black to black, and ground to ground.
This will mean one switch does nothing, while the other provides power to the remote. So you can swap out the double switch for a single one if you want.
Warning
This answer is a guess based on past experience, and the limited information you've provided. If you provide more information, we'll be able to provide more accurate answers. If you're unsure about what's going on, don't be afraid to contact an Electrician.
Best Answer
Preferred solution in that case is to attach the safety-ground wire to the box with a screw (if the box is metal), or wrap it around one of the fixture's mounting screws. As long as it makes a circuit to the box and the body of the fixture, it's doing it's job. (Of course if the fixture is non-conductive, it doesn't need grounding.)