Unifying keyboard and mouse dongle means that there is only one receiver for both of the wireless accessories instead of a receiver per accessory.
For example my wireless keyboard and mouse use one receiver that is plugged into one usb slot, whereas my previous ones each came with a receiver. One for my mouse and another for my keyboard. It took up two usb slots.
If like my old set it came as a set in one box it is more than likely possible for you to download a software dongle that will allow you to use the one that you have left for your mouse or keyboard. They have extremely close if not almost the same frequency that they send and receive data through and from your pc. Although you will only be able to use one at a time and use the program to switch between the two accessories.
I converted mine to Bluetooth with a Bluetooth dongle I had for my phone, but that's on a much more technical level and does require some knowledge and savvy or a background study in this area.
If I were you I would try the first option, if it doesn't work there are people on ebay selling their old receivers as to other difficulties as their pets using the wireless keyboard as chew toys and they are in turn stuck with the receiver.
If all above fails buy yourself a new set and be sure to leave the receiver in a port you will never use again and make it a temperament feature to that usb slot. Yes temperament!!! As if the pc will explode or melt if removed ever. That's all I have hope this leads you to a much less complicated choice!