We show the existence of nontrivial 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 $\{\nu_n\}$.