  In this work, we study the quasineutral limit of the one-dimensional
Vlasov-Poisson equation for ions with massless thermalized electrons. We prove
new weak-strong stability estimates in the Wasserstein metric that allow us to
extend and improve previously known convergence results. In particular, we show
that given a possibly unstable analytic initial profile, the formal limit holds
for sequences of measure initial data converging sufficiently fast in the
Wasserstein metric to this profile. This is achieved without assuming uniform
analytic regularity.
