Simple question:
If you connect 110v AC mains to a step down transformer, but nothing to the the outputs, what happens?

On one hand, you have a short, but on the other, the inductance of the transformer must limit the flow somewhat.

Does it blow the circuit breaker? Does the transformer heat up rapidly? Will the transformer catastrophically fail? Or does the impedance keep amperage levels well below trouble levels?

I'm planning on using the outputs to power a hot-wire foam cutter, and the cutting wire will break occasionally (which leaves the output side as an open circuit), I need to know what the danger level might be when that happens.

 

The primary will just use a lower amount of power when secondary is not connected to anything. It will just use what is called "magnetizing power". The power used by the primary varies by the secondary out put. Think of a phone charger, it doesn't burn out or cause problems when the phone isn't hooked up to it.