If you have done your own research to learn about any possible risks associated with liposuction, you may have come across fat embolism. Unfortunately, risks will always be associated with cosmetic procedures, but the chance of a fat embolism occurring is dramatically low. Trained surgeons and advancing technology make liposuction procedures far safer than they were in the past. Here is what you need to know about fam embolisms: What Are They? Fat embolisms are a mass substance that can break off your vein and travel through the blood vessel.