  Large magnification factors near gravitational lensing caustics of galaxy
cluster lenses allow the study of individual stars or compact stellar
associations at cosmological distances. We study how the presence of
sub-galactic subhalos, an inevitable consequence of cold dark matter, can alter
the property of caustics and hence change the interpretation of highly
magnified sources that lie atop them. First, we consider a galaxy cluster halo
populated with subhalos sampled from a realistic subhalo mass function
calibrated to $N$-body simulations. Then, we compare a semi-analytical
approximation and an adaptive ray-shooting method which we employ to quantify
the property of the caustics. As a case study, we investigate Earendel, a $z =
6.2$ candidate of magnified single or multiple star system with a lone lensed
image atop the critical curve in the Sunrise Arc. We find that the source size
constraint ($\lesssim 0.3\, \mathrm{pc}$) previously derived from macro lens
models should be relaxed by a factor of a few to ten when subhalos are
accounted for, therefore allowing the possibility of a compact star cluster.
The subhalos could introduce an astrometric perturbation that is $\lesssim
0.5''$, which does not contradict observation. These conclusions are largely
robust to changes in the subhalo population. Subhalos therefore should be
seriously accounted for when interpreting the astrophysical nature of similar
highly magnified sources uncovered in recent high-$z$ observations.
