  We study an admissible subcategory of the Bondal quiver which conjecturally
does not admit any Bridgeland stability conditions. Specifically, we prove that
its Serre functor coincides with the spherical twist associated with a
$3$-spherical object. As a consequence, we obtain a classification of the
spherical objects, deduce the non-existence of Serre-invariant stability
conditions, and construct a natural spherical functor from its structure as a
categorical resolution of the nodal cubic curve.
