There's no universal passive balanced to unbalanced converter that doesn't risk blowing up *something*. If you know what type of balanced output you have, then you can make one that works with *that*, but it's not necessarily safe for a different type.
Impedance-balanced is practically an unbalanced output, except that the resistor that is used to prevent it self-oscillating into a weird cable, is copied to the other wire in the balanced pair, and that resistor is grounded. This creates the same impedance on both wires, which makes them pick up noise equally, and that equal-noise is really the purpose of a balanced connection. When the receiver subtracts the two, the noise drops out, and you're left with the original signal.
If this is what you have, then you can just take the active wire as unbalanced and ignore the other.
Signal-balanced is practically two unbalanced outputs, with their anti-oscillation resistors, that always mirror each other. This gives twice the total swing for a given power supply - the signal is taken to be the *difference* between the two wires, not the isolated value of either one - and so a balanced receiver will be twice as "hot" when fed from one of these, compared to impedance-balanced.
If this is what you have, then you can take either wire as unbalanced and ignore the other. Which you choose determines the polarity: inverted or not.
Floating is...a little bit complicated. The original floating outputs were transformers, which use the same principle as a power transformer, but with different dimensions and materials to be nice for a wide range of frequencies, not just the one power-line frequency. That's the most flexible by far, but I doubt you have that because good transformers are *expensive*!
Instead, you might have an electronic floating output, which mimics that ability of a transformer. At first glance, it looks like signal-balanced, but an additional cross-connection allows either output to be held to something "solid" without trying to "break free", while the other output takes all the signal. Or if both connections are equally "stiff", then the signal will appear equally on both. It'll even handle both of its outputs getting yanked around the same way, while still pushing a signal out as a pure difference on top of that common-mode wiggle...and a balanced receiver will still take it just fine. The trouble is that each individual output is limited to its own power supply, whereas an actual transformer is not.
If this is what you have, then you must connect the unused wire to ground. Otherwise it'll take all the signal and the actual wire will not.
The reason that you can't have a universal passive converter is because of the conflicting requirements of floating and signal-balanced outputs. (impedance-balanced doesn't care) One requires that the unused wire be grounded, and the other can blow up if you ground that wire. (the resistor is not a high enough value to prevent that) If you have an isolated transformer, then you can connect one winding across the balanced output, and the other winding between the unbalanced input and its ground, effectively forcing a floating output, but I rather doubt you have one sitting around for the same reason that you don't have one inside the box: good ones are *expensive*!
