  This paper deals with the ${\mathcal C}^0$-rigidity of the reduction of
coiostropic submanifolds under the action of symplectic homeomorphism. More
precisely, we exhibit several situations where a symplectic homeomorphism that
takes a coisotropic submanifold to a smooth submanifold (which are then known
to be coisotropic by a result of Humili\`ere-Leclercq-Seyfaddini) abides to the
non-squeezing property in the reduction.
