  We investigate the stellar Mass-Metallicity Relation (MZR) using a sample of
637 quiescent galaxies with 10.4 <= log(M*/M ) < 11.7 selected from the LEGA-C
survey at 0.6 <= z <= 1. We derive mass-weighted stellar metallicities using
full-spectral fitting. We find that while lower-mass galaxies are both metal
-rich and -poor, there are no metal-poor galaxies at high masses, and that
metallicity is bounded at low values by a mass-dependent lower limit. This
lower limit increases with mass, empirically defining a MEtallicity-Mass
Exclusion (MEME) zone. We find that the spectral index MgFe = \sqrt{Mgb \times
Fe4383}, a proxy for the stellar metallicity, also shows a mass-dependent lower
limit resembling the MEME relation. Crucially, MgFe is independent of stellar
population models and fitting methods. By constructing the Metallicity
Enrichment Histories, we find that, after the first Gyr, the Star Formation
History of galaxies has a mild impact on the observed metallicity distribution.
Finally, from the average formation times, we find that galaxies populate
differently the metallicity-mass plane at different cosmic times, and that the
MEME limit is recovered by galaxies that formed at z >= 3. Our work suggests
that the stellar metallicity of quiescent galaxies is bounded by a lower limit
which increases with the stellar mass. On the other hand, low-mass galaxies can
have metallicities as high as galaxies ~1 dex more massive. This suggests that,
at log(M*/M ) >= 10.4, rather than lower-mass galaxies being systematically
less metallic, the observed MZR might be a consequence of the lack of massive,
metal-poor galaxies.
