  We study the escape dynamics in the presence of a hole of a standard family
of intermittent maps of the unit interval with neutral fixed point at the
origin (and finite absolutely continuous invariant measure). Provided that the
hole (is a cylinder that) does not contain any neighborhood of the origin, the
surviving volume is shown to decay at polynomial speed with time. The
associated polynomial escape rate depends on the density of the initial
distribution, more precisely, on its behavior in the vicinity of the origin.
Moreover, the associated normalized push forward measures are proved to
converge to the point mass supported at the origin, in sharp contrast to
systems with exponential escape rate. Finally, a similar result is obtained for
more general systems with subexponential escape rates; namely that the Ces\`aro
limit of normalized push forward measures is typically singular, invariant and
supported on the asymptotic survivor set.
