I don't know, maybe I'm misremembering, but back in Classic days we, rightly or wrongly, did it by actual dice - put each full dice in one characteristic or the other - doesn't work well with pluses and minuses obviously, but that is what I remember doing in about 1980ish (and applying it to the 3X5 card that was the character sheet).
Today, there's an advantage (besides the implied text that says you do so - but let's not pick at the sentence too much) of taking the second characteristic down to zero first in that the healing process is much simpler if you have at least one stat at full level since natural healing works better and you can avoid surgery.
So tactically, you either take the higher stat down to stay conscious longer, or, if it has a positive combat DM, choose to preserve it to get more hits in before you go down. But that's a recent thing, not a classic thing. In any case, once the shooting starts, you've usually already screwed up if they can shoot back....