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Let $X$ be a Noetherian, integral scheme. Let $\mathcal{F}$ be a torsion free sheaf on $X$ and let $U \subseteq X$ be the open subscheme where $\mathcal{F}$ is locally free.

Q. Is it true that $\mathrm{codim}_X(X\setminus U)\geq 2$?

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The answer is yes, assuming $X$ to be normal.

See S. Ishii, Introduction to singularities (Zbl 1308.14001), Proposition 5.1.7 p. 83.

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