  Using factorization homology, we realize the rational homology of the
unordered configuration spaces of an arbitrary manifold $M$, possibly with
boundary, as the homology of a Lie algebra constructed from the compactly
supported cohomology of $M$. By locating the homology of each configuration
space within the Chevalley-Eilenberg complex of this Lie algebra, we extend
theorems of B\"odigheimer-Cohen-Taylor and F\'elix-Thomas and give a new,
combinatorial proof of the homological stability results of Church and
Randal-Williams. Our method lends itself to explicit calculations, examples of
which we include.
