Hyperbolically embedded virtually free subgroups of relatively   hyperbolic groups
  We show that if a group is not virtually cyclic and is hyperbolic relative to a family of proper subgroups, then it has a hyperbolically embedded subgroup which contains a finitely generated non-abelian free group as a finite index subgroup. 
Yoshifumi Matsuda, Shin-ichi Oguni, Saeko Yamagata
math.GR math.GT