To a hyperbolic manifold one can associate a canonical projective structure
and ask whether it can be deformed or not. In a cusped manifold, one can ask
about the existence of deformations that are trivial on the boundary. We prove
that if the canonical projective structure of a cusped manifold is
infinitesimally projectively rigid relative to the boundary, then infinitely
many Dehn fillings are projectively rigid.