Cosmetic surgery is considered under the scale of surgeries a relatively safe operation. There are certain general rules that need to be followed in order to prevent and avoid complications. Death is rare with a Brazilian butt augmentation even though it seems there is a death in the news from butt augmentation every month. Most of these are due to the use of illicit products like liquid silicone.
Sudden death with a Brazilian butt lift is very rare. It can be secondary to a blood clot that originates from the leg.
Just recently in the Journal of Plastic and Reconstructive Surgery, a series of more than 300 cases was published. There were no deaths but two clots that resulted in pulmonary embolism that were resolved without major consequences.
What typically determines the risk of having problems will be your general well being. In other words, nobody is going to do a surgery if you have had an open-heart surgery, uncontrolled diabetes, COPD, if you were in a 100% oxygen or in a ventilator among others.
The risk of death is low if you are a low risk patient. The chance of having problems will be the same as if I were rolled over by a bus on my way to do a Brazilian butt lift.