  The environments of explosive transients link their progenitors to the
underlying stellar population, providing critical clues for their origins.
However, some Ca-rich supernovae (SNe) and short gamma ray burst (sGRBs) appear
to be located at remote locations, far from the stellar population of their
host galaxy, challenging our understanding of their origin and/or physical
evolution. These findings instigated models suggesting that either large
velocity kicks were imparted to their progenitors, allowing them to propagate
to large distances and attain their remote locations; or that they formed in
dense globular clusters residing in the halos. Here we show that instead, the
large spatial-offsets of these transients are naturally explained by the
observations of highly extended underlying stellar populations in (mostly early
type) galaxy halos, typically missed since they can only be identified through
ultra-deep/stacked images. Consequently, no large velocity kicks, nor halo
globular cluster environments are required in order to explain the origin of
these transients. These findings support thermonuclear explosions on
white-dwarfs, for the origins of Ca-rich SNe progenitors, and
no/small-natal-kicks given to sGRB progenitors. Since early-type galaxies
contain older stellar populations, transient arising from older stellar
populations would have larger fractions of early-type galaxy hosts, and
consequently larger fractions of transients at large offsets. This is verified
by our results for sGRBs and Ca-rich SNe showing different offset distributions
in early vs. late-type galaxies. Furthermore, once divided between early and
late type galaxies, the offsets' distributions of the different transients are
consistent with each other. Finally, we point out that studies of other
transients' offset distribution (e.g. Ia-SNe or FRBs) should similarly consider
the host galaxy-type.
