Is there a name for this kind of subcategory of an abelian category?

Question

I have encountered a full subcategory $\mathcal D$ of an abelian category $\mathcal C$ which satisfies the following property:

If

$$0 \to M' \to M \to M'' \to 0$$

is a short exact sequence in $\mathcal C$, then:

$(1)$ If at least one of $M',M''$ is contained in $D$, then $M$ is contained in $\mathcal D$.

$(2)$ If $M$ is contained in $\mathcal D$, then at least one of $M', M''$ is contained in $\mathcal D$.

I wonder if such a subcategory $\mathcal D$ has a name in the literature of abelian categories?