  In this paper, we study the solvability of a class of multi-dimensional
forward backward stochastic differential equations (FBSDEs) with oblique
reflection and unbounded stopping time. Under some mild assumptions on the
coefficients in such FBSDE, the existence result of adapted solutions is done
via a penalization method. The uniqueness is obtained by a verification theorem
similarly to the one used by Hu and Tang \cite{HT10}. Finally, we establish the
connection with the corresponding optimal switching problem. This latter is
solved by using the previous results on FBSDEs.
