I'm ready to stand corrected but I think the answer is:
In most cases a VOR and a DME are co-located.
For each VOR frequency there is a pre-defined DME frequency.
So when you tune the VOR/NAV receiver to a VOR frequency (VHF band), the DME transponder in the a/c is automatically tuned to the corresponding frequency in the 962 to 1213 MHz band.
So what happens in the case of your standalone DME on "112.500 MHz" is that the DME transponder is tuned to the correct DME frequency, even if the VOR receiver will not have a signal.