I couldn’t find anything in the manual that said this (it just says that the inputs and outputs are balanced), but I have both balanced (TRS) and unbalanced (TS) connections to the inputs on mine, and it seems to be fine. I’m pretty sure this will be the case with most audio interfaces, not something distinctive about the 16Rig.
Assuming you’re talking about line level signals from synths, drum machines, and the like, there’s no balanced vs. unbalanced switch.
If you want to connect unbalanced instrument cables from a guitar/bass or something similar that uses pickups and needs a high impedance input, you need to use the front panel inputs and switch them into INST mode using the menu on the device or the AudioFuse Control Center software.
I’m no electrical engineer, so my understanding of this might be simplistic, but as far as I know, connecting an unbalanced output to a balanced input with a TS cable “just works” without having to switch anything or explicitly detect anything, because it shorts the ring connector of the input to ground. The way balanced connections works means that this has no effect on the sound other than a lower input level compared with a balanced signal. You adjust for that using the output volume on the connected device or by adjusting the signal levels in software.
I think if you want to be really rigorous about it, you can use transformer/isolator devices that convert your unbalanced signal to a balanced one. I never have.
There’s another thread that discusses this kind of thing here:
Yes, exactly