© 2017. The American Astronomical Society. All rights reserved. We present the Palomar Transient Factory discoveries and the photometric and spectroscopic observations of PTF11kmb and PTF12bho. We show that both transients have properties consistent with the class of calcium-rich gap transients, specifically lower peak luminosities and rapid evolution compared to ordinary supernovae, and a nebular spectrum dominated by [Ca ii] emission. A striking feature of both transients is their host environments: PTF12bho is an intracluster transient in the Coma Cluster, while PTF11kmb is located in a loose galaxy group, at a physical offset ∼150 kpc from the most likely host galaxy. Deep Subaru imaging of PTF12bho rules out an underlying host system to a limit of MR > -8.0 mag, while Hubble Space Telescope imaging of PTF11kmb reveals a marginal counterpart that, if real, could be either a background galaxy or a globular cluster. We show that the offset distribution of Ca-rich gap transients is significantly more extreme than that seen for SNe Ia or even short-hard gamma-ray bursts (sGRBs). Thus, if the offsets are caused by a kick, they require higher kick velocities and/or longer merger times than sGRBs. We also show that almost all Ca-rich transients found to date are in group and cluster environments with elliptical host galaxies, indicating a very old progenitor population; the remote locations could partially be explained by these environments having the largest fraction of stars in the intragroup/intracluster light following galaxy-galaxy interactions.