Fat entering the bloodstream in clinically-significant amounts is extremely rare, and is not related to the type of liposuction performed, but more to the amount of fat removed and the number of areas treated.
Any ABPS-certified plastic surgeon will be able to explain the pros and cons of any elective cosmetic surgery, including fat embolism--a real but rare risk, but there are many "cosmetic surgeons" who have little or no training in plastic surgery, or are "board-certified" by bogus boards, who will decry legitimate fully-trained plastic surgeons who perform liposuction under general anesthesia and tell you that liposuction under local anesthesia is "safer."
This of course completely detours the discussion away from the fact that most (not all) local anesthesia liposuctions are performed by doctors that are NOT fully-trained ABPS-certified plastic surgeons (which is why they use local anesthesia--they do not have the availability of general anesthesia, which is usually the province of "real" surgeons with complete surgical privileges.)
Truly, this is one of those things that is low on the worry list--picking the right surgeon should be much, much higher! Best wishes! Dr. Tholen