  We put constraints on the properties of the progenitors of peculiar
calcium-rich transients using the distribution of locations within their host
galaxies. We confirm that this class of transients do not follow the galaxy
stellar mass profile and are more likely to be found in remote locations of
their apparent hosts. We test the hypothesis that these transients are from low
metallicity progenitors by comparing their spatial distributions with the
predictions of self-consistent cosmological simulations that include star
formation and chemical enrichment. We find that while metal-poor stars and our
transient sample show a consistent preference for large offsets, metallicity
alone cannot explain the extreme cases. Invoking a lower age limit on the
progenitor helps to improve the match, indicating these events may result from
a very old metal-poor population. We also investigate the radial distribution
of globular cluster systems, and show that they too are consistent with the
class of calcium-rich transients. Because photometric upper limits exist for
globular clusters for some members of the class, a production mechanism related
to the dense environment of globular clusters is not favoured for the
calcium-rich events. However the methods developed in this paper may be used in
the future to constrain the effects of low metallicity on radially distant
core-collapse events or help establish a correlation with globular clusters for
other classes of peculiar explosions.
