  Renault proved in 2008 that if $G$ is a topologically principal groupoid,
then $C_0(G^{(0)})$ is a Cartan subalgebra in $C^*_r(G, \Sigma)$ for any twist
$\Sigma$ over $G$. However, there are many groupoids which are not
topologically principal, yet their (twisted) $C^*$-algebras admit Cartan
subalgebras. This paper gives a dynamical description of a class of such Cartan
subalgebras, by identifying conditions on a 2-cocycle $c$ on $G$ and a
subgroupoid $S \subseteq G$ under which $C^*_r(S, c)$ is Cartan in $C^*_r(G,
c)$. When $G$ is a discrete group, we also describe the Weyl groupoid and twist
associated to these Cartan pairs, under mild additional hypotheses.
