The collapse conjecture for expected dimension with sparse collapsed graph

Let $G$ be a graph with $n$ vertices and at most $2n-2$ edges with an exchange, and let $G'$ be the resulting collapsed graph. The collapse conjecture. If $G'$ has $n-1$ edges, then $G$ has the expected dimension if and only if $G'$ has the expected dimension. This is a proposed preservation principle for the expected dimension under collapsing an exchange when the collapsed graph has $n-1$ edges. The supplied text gives no resolution, so the conjecture remains open.