Risk of Death from Liposuction?

Many procedures that require anesthesia have some risk of death. The risk may be very rare or less rare. The particular figure you are quoting probably never existed even at the height of the rash of deaths associated with liposuction in the 90's.
These coincided with a trend to do liposuction with ultrasonic suction aspirators that required significant infiltration of wetting solution into the fat to avoid a tissue burn and higher volumes of liposuction. The wetting solution contained local anesthetic and when combined with the drugs for general anesthesia, the combination proved to be lethal.
With the Medical Boards of Florida and California leading the way, and recognition on the part of plastic surgeons that this was bad business, limits were placed on the volume of liposuction done at one time. This has helped reduced the incidence of liposuction related deaths.
The one in 5000 case incidence which is extremely high came from a survey study of general plastic surgeons and probably grossly overestimates the death rate. However other studies suggest that the rate is about 1 in 30,000 to 1 in 50,000 cases.
To put this in perspective the risk of dying on a commuter aircraft is about 1:500,000. So these numbers should no be dismissed lightly. If a surgeon tells you that "it has never happened to me in X years of practice," take this with a grain of salt. The incidence even at 1:5000 cases that many surgeon will practice an entire career without experiencing this complication.
Now there is an alternative to having liposuction under general anesthesia. When liposuction is performed under local anesthesia there are virtually no operative deaths. The incidence of death from this type of liposuction is about 1:500,000. Who performs liposuction under local anesthesia? Dermatologic surgeons. Using this method called tumescent liposuction, you can have liposuction safely performed with almost no risk of death.

 I have been doing liposuction for more than 30 years. We have never had any serious complication. No deaths, embolus,infection, bleeding. As long as the total amount remove is under 5 liters.