  The discovery of the $Z_c(3900)^\pm$ and $Z_b(10610)^\pm$ structures in the
heavy quarkonium spectrum showed the need to incorporate hadron structures
beyond the naive $qqq$ and $q\bar q$ systems in quark models. The new charged
structure called $Z_{cs}(3985)^-$, spotted in the $K^+$ recoil-mass spectrum
close to the $D^-_s D^{*0}/D^{*-}_sD^0$ threshold, is a new evidence in this
line. In this work, we analyze the $Z_{cs}(3985)^-$ state, following the
calculation of the $Z_c$ and $Z_b$ states using a chiral constituent quark
model in a coupled-channels calculation, with all the parameters constrained
from previous calculations. The pole structure of the S-matrix shows two
virtual poles below the $D_s^-D^{*\,0}$ and $D_s^{*\,-}D^{*\,0}$ thresholds
compatible with the $Z_{cs}(3985)^\pm$ and a new predicted $Z_{cs}(4110)^\pm$
structure, the SU(3) flavor partner of the $Z_c(4020)^\pm$. The $K^+$
recoil-mass spectrum is calculated in good agreement with LHCb and BESIII
experimental data, with no fine tuning of the model parameters. Our results
indicate that the $Z_{cs}(3985)^\pm$ and $Z_{cs}(4000)^\pm$ signals originate
from the same virtual state.
