  Given a partial action $\alpha=(A_g,\alpha_g)_{g\in \mathcal{G}}$ of a
connected groupoid $\mathcal{G}$ on a ring $A$ and an object $x$ of
$\mathcal{G}$, the isotropy group $\mathcal{G}(x)$ acts partially on the ideal
$A_x$ of $A$ by the restriction of $\alpha$. In this paper we investigate the
following reverse question: under what conditions a partial group action of
$\mathcal{G}(x)$ on an ideal of $A$ can be extended to a partial groupoid
action of $\mathcal{G}$ on $A$? The globalization problem and some applications
to the Morita and Galois theories are also considered, as extensions of similar
results from the group actions case.
