Couple of points here,
Under UK law, The Health and Safety at Work Act (HASAWA) which closely follows European Parliament requirements there is a hazard.
I assume that in the litigious US of A there is similar legislation, and likely as not it will be tougher than ours.
All employers have a duty of care to their employees and must demonstrate this by maintaining records of all safety related issues.
All equipment must be assessed for risks to health and safety and all tasks carried out by employees in the business of their employer must also be assessed.
More specifically, in the case of electrical equipment, this must be inspected and tested regularly for continuing suitability for safe operation.
In the real world this means that everything in the building has to be tested before being allowed on site, so if an employee brings, ooooh lets say an electric fan to work, this must not be used until it has been tested and approved using very specific methodology, by staff who have been certified as being competant for this task.
Not only must every appliance be tested, but records have to be kept to prove that this has been done in accordance with a regular inspection and maintenance program, which will vary according to the duty of the appliance.
Even if you are not a direct employee, the owner of the site must ensure that the environment provided is safe.
Now to get much more specific, the fan itself.
The vast majority of these lightweight fans have rotors that run in plain brass bushes and these are lubricated at manufacture with bearing grease, which stays there for the life of the fan.
Problem is that when you run such a fan, or any fan for that matter, it will get warm and soften the grease, turn the fan off and the grease cools down.
Repeat this cycle day in day out and the grease age hardens, causing more drag on the fan rotor, which in turn gets warmer and in turn causes the grease to deteriorate more.
So what! you say,
Well the drag on the rotor eventually causes it to get so hot that a thermal fuse melts (a special type of fuse that melts at a specific temperature rather than the better known current operated fuse) and open-circuits the motor, thus the fan will not run.
All seems well, but it is not unknown for that thermal fuse not to work at all, and the fan is then able to reach a temperature which is dangerous, and may set light to the plastic casing. If this happens when you are on your lunch break or have left the building then this could be serious.
The other thing that happens is that some people with a little electrical knowledge will work out why a fan has failed and bypass the thermal fuse and without this protective device, the risk of fire is greatly increased.
I would think that this employer will not allow staff to bring in any electrical equipment unless it has been checked out first, but in any case, fans are a particular hazard and do cause fires.