Generally, liposuction under local anesthesia is practiced by physicians who are not board certified as plastic surgeon and don't have hospital privileges or properly accredited surgery center privileges.
The incidence of death is very rare. The risk of complications is more commonly associated with lack of credentialing on part of the facilities and the practitioner. Be sure to ask about board certification and what specialty in particular. Remember there is no such thing as a board of cosmetic surgery. You should also be aware of which hospital and surgery centers your surgeon is working with.Best of luck! Dr. Boschert