Let $\scr{F}$ be a coherent sheaf on a smooth $3$-dimensional algebraic variety $X$ over an algebraically closed field $k$ of characteristic $0$. Suppose that $\scr{F}$ fails to be locally free at only finitely many points of $X$, called "bad" points. Under what conditions on $\scr{F}$ does there exist a unique locally free sheaf $\scr{F}'$ that agrees with $\scr{F}$ away from the "bad" points?
(In the $2$-dimensional case, the answer is the double-dual sheaf $\scr{F}^{\vee\vee}$.)