  Let $Z$ be the transient reflecting Brownian motion on the closure of an
unbounded domain $D\subset {\mathbb R}^d$ with $N$ number of Liouville
branches. We consider a diffusion $X$ on $\overline D$ having finite lifetime
obtained from $Z$ by a time change. We show that $X$ admits only a finite
number of possible symmetric conservative diffusion extensions $Y$ beyond its
lifetime characterized by possible partitions of the collection of $N$ ends and
we identify the family of the extended Dirichlet spaces of all $Y$ (which are
independent of time change used) as subspaces of the space ${\rm BL}(D)$
spanned by the extended Sobolev space $H_e^1(D)$ and the approaching
probabilities of $Z$ to the ends of Liouville branches.
