  We estimate the stochastic gravitational wave spectrum emitted from a network
of cosmic strings in which the latter are effectively stable against breaking
by monopole pair creation. The monopoles are produced at a higher scale from an
earlier symmetry breaking and experience significant inflation before
reentering the horizon. This gives rise to monopole-antimonopole pairs
connected by string segments and the string loop formation essentially ceases.
As a consequence, the lower frequency portion of the gravitational wave
spectrum is suppressed relative to the no-inflation case with stable strings,
which evades the stringent PPTA bound on the dimensionless string tension
$G\mu$. We display the modified spectrum, accessible in the ongoing and future
experiments, for $G\mu$ values in the range $10^{-10} - 10^{-15}$. We show how
this `quasi-stable' string network is realized in realistic grand unified
theories.
