A circuit breaker can trip (or a fuse can blow) due to nothing more than a loose wire. This can happen even if the wire is still connected to an outlet, but the outlet's terminal screw isn't tightened enough. In other situations, completely loose wires can come in contact with electrical boxes or other wires, possibly resulting in a tripped breaker—or worse.
Loose and disconnected wires can become hot enough to start fires or can create serious shock hazards because the breaker doesn't always trip and shut off the power.
Dangers of a Loose Connection
Wires connect to outlets—properly called receptacles—with screw terminals or other devices to provide a secure connection. Wires that are tight to the terminal make good electrical contact that the electricity can pass through with minimal resistance. But if the terminal is not tight, and the wire is not compressed against the terminal's metal contact, there is greater resistance. And resistance creates heat. The looser the connection, the greater the heat.
If the heat from a loose connection is great enough or sustained long enough, it can trip the circuit's breaker, though often it does not. A normal breaker is designed only to trip when the load is too great or when the electrical path is shorted (a short circuit). The tricky part is, you might not notice any problem in the circuit. For example, a reader wrote in with a story about his electric dryer, which worked fine but periodically turned off because the breaker tripped. This being a dedicated circuit (supplying only one appliance), there were no other receptacles or connections on the circuit, so the tripped breaker wouldn't be due to an overload.
As it turns out, the reader was an electrical engineer, and he ultimately discovered that one of the terminals on the dryer's receptacle just needed some tightening. The dryer still worked because the wire was connected, but eventually, the wire would heat up enough—through resistance—to trip the breaker. Tightening the terminal solved the problem.
Loose Wires Can Cause Arching
The engineer's wiring certainly heated up from increased resistance, but it also may have been subject to arching, which can create even more heat. Arching can occur in a few different ways, but in essence, it's electricity jumping from one conductor (like a hot wire) to another conductor (like a receptacle terminal or another wire or conductive material).
In the engineer's case, the arching would occur between the "hot" wire and its terminal. This is an example of a series arc fault, in which the electricity is following its intended path, but it's meeting a lot of resistance due to the lack of a good electrical connection.
Another type of arching occurs when a hot wire touches a neutral wire or a ground wire. This is called a parallel arc fault and can be caused by (among other things) loose wires that touch other wires inside an electrical box.
Breakers Don't Always Catch Bad Connections
A loose wiring connection may or may not trip a standard circuit breaker. This is one reason why new homes today must have special breakers called arch-fault circuit-interrupters, or AFCIs. These are designed to detect the most common types of arc faults in home wiring and shut off the power. In short, AFCIs help protect against house fires caused by arc faults.
AFCI protection is required on circuits serving bedrooms, hallways, living rooms, and most other living areas in a home with recent code requirement updates. Previously, they were only required in bedrooms.
AFCIs are different from GFCIs (ground-fault circuit-interrupters), which are required in bathrooms, kitchens, garages, outdoors, and other areas where moisture may be present. Under current rules, virtually every circuit in a new home is protected by an AFCI or GFCI, depending on the application.
Sweeting, David. "Arcing faults in electrical equipment." IEEE Transactions on industry applications 47.1 (2010): 387-397.