How does an inverting op-amp feeds back 0 volts when the Vout is not 0
In an inverting amplifier it is the current between the output and the inverting input that achieves negative feedback. The voltage at \$V_{OUT}\$ changes so that the voltage difference between the inverting and non-inverting inputs will become very small, ideally zero. When this happens, 
the current flowing through the feedback resistor will be just equal to the current flowing through the input resistor. If the non-inverting input happens to be connected to ground then the voltage at the inverting input will also be essentially zero.

EDIT: To clarify, I'm talking mostly about ideal op amp behavior. Check the specifications of any real op amp to ensure that the output swings all of the way to ground.