  Calcium-rich supernovae represent a significant challenge for our
understanding of the fates of stellar systems. They are less luminous than
other supernova (SN) types and they evolve more rapidly to reveal nebular
spectra dominated by strong calcium lines with weak or absent signatures of
other intermediate- and iron-group elements, which are seen in other SNe.
Strikingly, their explosion sites also mark them out as distinct from other SN
types. Their galactocentric offset distribution is strongly skewed to very
large offsets (around one third are offset greater than 20 kpc), meaning they
do not trace the stellar light of their hosts. Many of the suggestions to
explain this extreme offset distribution have invoked the necessity for unusual
formation sites such as globular clusters or dwarf satellite galaxies, which
are therefore difficult to detect. Building on previous work attempting to
detect host systems of nearby Ca-rich SNe, we here present Hubble Space
Telescope imaging of 5 members of the class - 3 exhibiting large offsets and 2
coincident with the disk of their hosts. We find no underlying sources at the
explosion sites of any of our sample. Combining with previous work, the lack of
a host system now appears to be a ubiquitous feature amongst Ca-rich SNe. In
this case the offset distribution is most readily explained as a signature of
high-velocity progenitor systems that have travelled significant distances
before exploding.
