Matroid Theory Terminology - What is the name of independent sets which can be extended to be dependent but are not a superset of another such set?

Question

Let $M=(I,E)$ be a matroid of ground set I and independent sets E.

I am now looking for a term for all those sets $X\subseteq I$ such that there exists an element $e$ which fulfills the following properties:

1. $e\in I\setminus X$
2. $X\cup \{e\} \notin E$
3. and there exists no other set $Y$ with the first 2 properties and $Y \subseteq X$

More colloquially said those sets for which an element exists that would make the set dependent but none of its subsets can be extended in this manner.

If there is no name for it, are there similar concepts in independence systems or other combinatorial studies?