Electric wall heaters typically have a fuse that breaks if the unit draws too much electricity due to a power surge. Some also have temperature-based fuses to turn the unit off if it gets too hot.
The biggest threat posed by wall heaters is the potential to light fires. Because of this, wall heaters typically have front covers that allow air to flow out of the unit while also preventing items from entering its hot interior. Insulation is used on the exterior of the unit to keep heat from leaking out of the system, and this insulation also protects the surrounding walls from burning and catching fire.