  For any finitely generated, non-elementary, torsion-free group $G$ that is
hyperbolic relative to $\mathbb P$, we show that there exists a group $G^*$
containing $G$ such that $G^*$ is hyperbolic relative to $\mathbb P$ and $G$ is
not relatively quasiconvex in $G^*$. This generalizes a result of I. Kapovich
for hyperbolic groups. We also prove that any torsion-free group $G$ that is
non-elementary and hyperbolic relative to $\mathbb P$, contains a rank 2 free
subgroup $F$ such that the group generated by "randomly" chosen elements
$r_1,...,r_m$ in $F$ is aparabolic, malnormal in $G$ and quasiconvex relative
to $\mathbb P$ and therefore hyperbolically embedded relative to $\mathbb P$.
