  We show the existence of non-trivial quasi-stationary measures for
conservative attractive particle systems on $\ZZ^d$ conditioned on avoiding an
increasing local set $\A$. Moreover, we exhibit a sequence of measures
$\{\nu_n\}$, whose $\omega$-limit set consists of quasi-stationary measures.
For zero range processes, with stationary measure $\nur$, we prove the
existence of an $L^2(\nur)$ nonnegative eigenvector for the generator with
Dirichlet boundary on $\A$, after establishing a priori bounds on the
$\{\nu_n\}$.
