You can have an Aspect that's bad or negative. "Weak," for example.

Why would you do this?

First, it provides color, story fodder, something interesting.

Second, it's hard to come up with many aspects that are always negative. Being "Weak" might arguably cause people to underestimate you, cause you to be chosen last to voluteer for stuff, etc.

Third, while "Weak" is always there, if it's going to cause you an actual problem against your will, the GM has to call you on it and offer you Fate Points to force you into it. Of course, you can still deny it -- but it will cost you Fate Points in that case to do it ...

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Character Rules