  Self-destructive percolation with parameters $p,\delta$ is obtained by taking
a site percolation configuration with parameter $p$, closing all sites
belonging to infinite clusters, then opening every closed site with probability
$\delta$, independently of the rest. Call $\theta(p,\delta)$ the probability
that the origin is in an infinite cluster in the configuration thus obtained.
For two-dimensional lattices, we show the existence of $\delta>0$ such that,
for any $p>p_c$, $\theta(p,\delta)=0$. This proves the conjecture of van den
Berg and Brouwer [Random Structures Algorithms 24 (2004) 480-501], who
introduced the model. Our results combined with those of van den Berg and
Brouwer [Random Structures Algorithms 24 (2004) 480-501] imply the nonexistence
of the infinite parameter forest-fire model. The methods herein apply to site
and bond percolation on any two-dimensional planar lattice with sufficient
symmetry.
