Dense-copy conjecture for nonabelian limit groups

Let $G$ be a locally compact group, and let $F_2$ denote the free group of rank two. A group has a dense copy in $G$ if it contains a subgroup isomorphic to that group whose image is dense in $G$. Dense-copy conjecture. If $G$ has a dense copy of $F_2$, then $G$ admits a dense copy of every nonabelian limit group. This conjecture proposes that locally compact groups containing a dense free subgroup of rank two also contain dense copies of all nonabelian limit groups, extending the known results for certain classes of groups; its general status is not specified in the source.