  Small forcing always ruins the indestructibility of an indestructible
supercompact cardinal. In fact, after small forcing, any cardinal $\kappa$
becomes superdestructible---any further ${<}\kappa$-closed forcing which adds a
subset to $\kappa$ will destroy the measurability, even the weak compactness,
of $\kappa$. Nevertheless, after small forcing indestructible cardinals remain
resurrectible, but never strongly resurrectible.
