The discovery of long-lived, ubiquitous, X-ray emitting hot galactic coronae in groups and clusters by Chandra poses a challenge to our understanding of galactic ISM survival in harsh environments. These coronae are unique probes of ICM and ISM microphysics, since their survival depends on a delicate balance between external ICM physical processes that can alternatively destroy or replenish these coronae and internal galactic physics that can replenish them. In this talk, I present MHD simulations of the evolution of hot coronae of cosmological populations of galaxies in group and cluster environments. I summarize the effects of external ICM phenomena, paritcularly tidal and ram pressure stripping and shielding by magnetic fields on the survival of these coronae. I also present synthetic X-ray observations which I use to motivate a stacking analysis on combined optical and X-ray surveys to quantify the effect of the local environment on galactic coronae. Finally, I will briefly summarize my future planned theoretical efforts in understanding the overall fate of the multiphase ISM in cluster galaxies.