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Supernovae and other stellar explosions (SNe) play key roles in galaxy formation and enrichment. Marking a stellar death comma they are critical to understanding stellar evolution. Cosmologists use SNe to measure the Universe.s expansion. Some SNe produce neutron stars and black holes. For these reasons and many others comma including interesting physics of the explosions themselves comma understanding the progenitors and explosions of all variety of SNe is of great importance to astrophysics. Late-time (>200 days after explosion) HST observations of SNe measure the amount of radioactive material generated in the explosion and probe the circumstellar environments of the progenitor systems at radii inaccesible through other means. These same images can be used to examine the SN environment comma and from nearby stars comma we can constrain the progenitor star.s age. For all transients comma these data reveal their late-time luminosity comma constraining explosion physics and what powers them. These observations will also precisely determine the SN position comma allowing future observations to search for companion stars. For SNe Iax comma which are thought to not disrupt their white dwarf progenitor stars comma we can detect the surviving star when leftover radioactive material forces it to the Eddington limit. Finally comma late-time observations of TDEs can see the accretion disk hidden earlier. We have assembled a sample of 75 recent comma well-observed transients comma that are sufficiently close that this science can be done with short HST exposures. Combined with the statistical nature of these studies comma this program is perfectly matched to snapshot observations.