  Low-metallicity very massive stars with an initial mass of $\sim 140$--$260\,
{\rm M_\odot}$ are expected to end their lives as pair-instability supernovae
(PISNe). The abundance pattern resulting from a PISN differs drastically from
regular core-collapse supernova (CCSN) models and is expected to be seen in
very metal-poor (VMP) stars of ${\rm[Fe/H]}\lesssim -2$. Despite the routine
discovery of many VMP stars, the unique abundance pattern expected from PISNe
has not been unambiguously detected. The recently discovered VMP star LAMOST
J1010+2358, however, shows a peculiar abundance pattern that is remarkably well
fit by a PISN, indicating the potential first discovery of a bonafide star born
from gas polluted by a PISN. In this paper, we study the detailed
nucleosynthesis in a large set of models of CCSN of Pop III and Pop II star of
metallicity ${\rm[Fe/H]}=-3$ with masses ranging from $12$--$30\,{\rm
M_\odot}$. We find that the observed abundance pattern in LAMOST J1010+2358 can
be fit at least equally well by CCSN models of $\sim 12$--$14\,{\rm M_\odot}$
that undergo negligible fallback following the explosion. The best-fit CCSN
models provide a fit that is even marginally better than the best-fit PISN
model. We conclude the measured abundance pattern in LAMOST J1010+2358 could
have originated from a CCSN and therefore cannot be unambiguously identified
with a PISN given the set of elements measured in it to date. We identify key
elements that need to be measured in future detections in stars like LAMOST
J1010+2358 that can differentiate between CCSN and PISN origin.
