  We examine binary systems where the more massive star, the primary, explodes
as a core collapse supernova (CCSN) the secondary star is already a giant that
intercepts a large fraction of the ejecta. The ejecta might pollute the
secondary star with newly synthesized elements such as calcium. We use Modules
for Experiments in Stellar Astrophysics (MESA) to calculate the evolution of
such SN-polluted giant (SNPG) binaries. We estimate that on average at any
given time tens of SNPGs are present in the Galaxy, and $\approx 10$ SNPG
objects are present in the Magellanic Clouds. We speculate that the high
calcium abundance of the recently discovered evolved star HV2112 in the Small
Magellanic Cloud might be the result of an SNPG with a super AGB stellar
secondary of a mass $\approx 9 M_\odot$. This rare SNPG scenario is an
alternative explanation to HV2112 being a Thorne-{\.Z}ytkow object (TZO).
