  Weak cosmic censorship conjecture (WCCC) is a basic principle that guarantees
the predictability of spacetime and should be valid in any classical theories.
One critical scientific question is whether the WCCC can serve as a constraint
to the gravitational theories. To explore this question, we perform the
first-order Sorce-Wald's gedanken experiments to test the WCCC in the
higher-order gravitational theories and find that there exists a destruction
condition $S_\text{ext}'(r_h)<0$ for the extremal black holes. To show the
power of this condition, we evaluate the constraints given by WCCC in the
quadratic and cubic gravitational theories. Our investigation makes an
essential step toward applying WCCC to constrain the modified gravitational
theories, and opens a new avenue to judge which theory is reasonable.
