  We show that a surface group of high genus contained in a classical simple
Lie group can be deformed to become Zariski dense, unless the Lie group is
$SU(p,q)$ (resp. $SO^* (2n)$, $n$ odd) and the surface group is maximal in some
$S(U(p,p)\times U(q-p))\subset SU(p,q)$ (resp. $SO^* (2n-2)\times SO(2)\subset
SO^* (2n)$). This is a converse, for classical groups, to a rigidity result of
S. Bradlow, O. Garc\'{\i}a-Prada and P. Gothen.
