Does this propetry $A\subseteq f(A)$ have a name?

Question

Let $f:X\to X$. If $S\subset X$ is such that $f(S)\subseteq S$, the set $S$ is called $f$-invariant.

But what if $$A\subseteq f(A)$$ holds for some $A\subset X$? Does this property of the set $A$ have a name?

Answer 1

One says that $f$ is extensive for $A$. See e.g. https://en.wikipedia.org/wiki/Closure_operator.