$I=mI$, when $I$ is not finitely generated.

Question

Let $(R,m)$ be a commutative local ring with unit. Suppose $I$ is an ideal (not finitely generated). If $I=mI$, what can we say about $I$?

If $I$ were finitely generated, then Nakayama's lemma would imply $I=0$, so I am interested in the case when $I$ is not finitely generated.

Any reference would be appreciated. Thanks