If anyone could answer this and provide a source I would appreciate it.
until it melts or shorts out
As long as the wire is intact, it will conduct. The ability to conduct electricity will be interrupted the moment the molecules of the wire separate, from heat if the fire is hot enough to melt the conductor, and cause a breach in the conductor. Current flow stops, no circuit.
(Quoted from source): Most homes have two incoming voltages: 120 volts for lighting and appliance circuits and 240 volts for larger air conditioning and electric dryer circuits. When an appliance switch is turned on, electrical current flows through the wire, completing the electrical circuit and causing the appliance to operate. The amount of flowing current is called amperage. Most lighting circuits in the home are 15 amp circuits. Most electric dryers and air conditioners require larger 30 amp circuits. The amount of electrical power needed to make an appliance operate is called wattage and is a function of the amount of current flowing through the wire (amperage), and the pressure in the system (voltage). Mathematically speaking, volts x amps watts. So, if we have a 120 volt system and a 15 amp current, we can flow a maximum of 120 x 15 or 1,800 watts on a typical lighting or appliance circuit. When too many lights or appliances are attached to the electrical system, it will overload and overheat. This can cause the wire insulation to melt and ignite, resulting in an electrical fire. The amount of electrical current flowing through wire is affected by resistance. This is known as ohms. Resistance causes increased heat in the wire. Heat is the byproduct that makes some appliances work, such as an iron, toaster, stove or furnace. Large current faces high resistance when moving through a small wire. This generates lots of heat. That's how an incandescent light bulb works. Resistance through the light filament causes it to heat up which gives off a bright light. Electrical resistance also is affected by the length of a wire. Operating an electrical hedge clipper with a long extension cord increases resistance and might cause the cord to overheat, melt or ignite. The same occurs if too many strands of Christmas lights are connected together.