  For a free group $\mathbb{F}$ of finite rank such that
$\text{rank}(\mathbb{F})\geq 3$, we prove that the set of weak limits of a
conjugacy class in $\mathbb{F}$ under iterates of some hyperbolic
$\phi\in\mathsf{Out(\mathbb{F})}$ is equal to the collection of generic leaves
and singular lines of $\phi$. As an application we describe the ending
lamination set for a hyperbolic extension of $\mathbb{F}$ by a hyperbolic
subgroup of $\mathsf{Out(\mathbb{F})}$ in a new way and use it to prove results
about Cannon-Thurston maps for such extensions. We also use it to derive
conditions for quasiconvexity of finitely generated, infinite index subgroups
of $\mathbb{F}$ in the extension group. These results generalize similar
results obtained by Mahan Mj, Kapovich-Lustig and use different techniques.
