  In this paper we generalize a theorem of M. Hilsum and G. Skandalis stating
that the $C^*$- algebra of any foliation of non zero dimension is stable.
Precisely, we show that the C*-algebra of a Lie groupoid is stable whenever the
groupoid has no orbit of dimension zero. We also prove an analogous theorem for
singular foliations for which the holonomy groupoid as defined by I.
Androulidakis and G. Skandalis is not Lie in general.
