  We estimate the stellar mass that satellite galaxies lose once they enter
groups (and clusters) by identifying groups in a high-resolution cosmological
N-body simulation, assigning entry masses to satellite galaxies with halo
abundance matching at the entry time, and comparing the predicted conditional
stellar mass function of satellite galaxies at $z\simeq0$ with observations.
Our results depend on the mass of the stars that form in satellite galaxies
after the entry time. A model in which star formation shuts down completely as
soon a galaxy enters a group environment is ruled out because it underpredicts
the stellar masses of satellite galaxies even in the absence of tidal
stripping. The greater is the stellar mass that is allowed to form, the greater
the fraction that needs to be tidally stripped. The stellar mass fraction lost
by satellite galaxies after entering a group or cluster environment is
consistent with any value in the range $0-40\%$. To place stronger constraints,
we consider a more refined model of tidal stripping of galaxies on elongated
orbits (where stripping occurs at orbit pericentres). Our model predicts less
tidal stripping: satellite galaxies lose $\sim 20-25\%$ of their stellar mass
since their entry into the group. This finding is consistent with a
slow-starvation delayed-quenching picture, in which galaxies that enter a group
or cluster environment keep forming stars until at least the first pericentric
passage.
