Balanced circuits were developed in the age before opamp chips. There was a transformer at each end. Pins two and three were connected across the secondary of the outputting device and the primary of the inputting device. So if you did not ground pin 3 you had no sound at all. If you grounded pin two, then phase was reversed.
Transformers are still around, and quite a few balanced inputs and outputs use them. Now the usual practice is to balance using dual op amp chips, for input and output. Pin 2 goes to one half and three to the other. So if you leave a line not connected, you get no signal from one half of the op amp chip, with quote a few circuits, and actually the best ones.
Balanced circuits were developed in the broadcast and engineering industries, many, many years ago. The reason was noise prevention, especially RF penetration. The long cables, will pick up identical interference. So the interference arriving at the primary connected to pins 2 and 3 cancel in the primary of the transformer.
If the circuit in a modern piece of equipment is a true replica of the transformer balanced circuit, there will be problem if pin three is not grounded. I would always connect pin three to ground, when going from balanced to unbalanced, or better yet, balance the unbalanced output with a transformer. Radio Shack sell very high quality transformer adapters for doing just that.