I had this exact same conversation with one of my players. Basically, the answer is, there's no sane reason to do this on the skill sheet directly; this belongs purely as an Aspect, or simply as non-statted fluff.
Reason being: Remember the extremely course granularity of the skill system. Each jump on the scale is fairly significant, since 0 somewhat represents 'random person on the street asked to do something under pressure they probably aren't used to doing that way', and +5 represents 'damn near peak of potential absent other assistive factors'.
Conversely, considering that it's possible to get as much as a shift of 4 either way on your 4dF roll, someone with a base +0 is perfectly capable of doing absurdly horribly already. An intentional drop below mediocre isn't really going to significantly alter results in any real circumstances where the test actually matters. Considering the grade of tests even Feet in the Water tends to get when a roll is actually needed, if you were likely to fail with -1, it's probable you would have failed with +0 as well. Success or failure under those circumstances depends more on the application Aspect invocations and tags more than anything else.
And if being sucky ata particular thing is truly important to the character concept... well, here in Fate land, we use Aspects for things like that, not merely skill points.
After discussing all THAT, if someone still wants to do it, they're probably trying to min-max, since the skills dropped below Mediocre were certainly ones they didn't intend to rely on anyway.
In my opinion, that kind of intent is more than slightly antithetical to a narrative-focused game system like this.
