Old house ceiling has unused brown wire, what is it for?
Ceiling fans tend to also have lights integrated with then and you want to control the separately. This is why 2 live wires are often run from the switch to the fan. 

To check you can open the switch that controls the fan and see if a matching wire is present and has continuity to the wire in the ceiling box.

It is safe to leave it disconnected. However I suggest you cap it off with a wire nut at both ends to avoid the copper inside from touching something it shouldn't.