The fixed-element settlement conjecture for representable matroids

Let $M$ be a representable matroid and let $e$ be an element of $M$. The deletion $M{-} e$ settles $M$ when representations of $M{-} e$ determine representations of $M$ in the relevant sense, and $e$ is fixed in $M$ when its representation is forced by the remaining structure. Fixed-element settlement conjecture. $M{-} e$ settles $M$ if and only if $e$ is fixed in $M$.

The conjecture is motivated by the relationship between the Settlement Theorem and free expansions. The source does not provide a resolution.