If you have only the positive cable connected to the battery, and the negative cable floating in the air, then you take your voltmeter and touch between the negative cable and the negative battery terminal, you should be reading 12.76 volts if the Negative (black) meter lead is on the battery and the positive (red) meter lead is on the negative cable. If you have the black meter lead on the negative cable and the red lead on the negative battery terminal, you’ll read the same voltage, but reverse the polarity, so it will be -12.76.
What’s the issue? Sounds normal to me. If your friend’s battery keeps dying, and it is over 3 years old, it’s time for a new battery. they make them so cheap these days that you’re lucky to get three years out of a battery. If it is a sealed type, replace it. If it is a non sealed type, pry open the caps and make sure the cells are filled with DISTILLED water to the indicator mark, or at minimum so that all of the plate material is under water by at least 1/4”.
Can you give the reason for using distilled water?