Risk of Death from Injectable Fillers Due to Embolism?

The type of embolism you're referring to is caused by injection of a foreign substance like filler into a blood vessel which causes a clot to form which can break off and then travel in the bloodstream causing damage.  Since this involves the skin (and not an embolism of the lungs or heart), it is unlikely to result in death, but more likely to result in necrosis (due to lack of oxygen to the skin which can result in the tissue dying) and resultant scarring and nerve damage.  This is particularly high risk around the eye area because an embolism could result in blindness. This is why nonphysicians and non-core trained specialists are advised to stay away from injecting in these higher risk regions. There are especially rich arcades of blood vessels in the infraorbital region and forehead, glabella and nasal region that are higher risk for embolism.This is something that is discussed amongst physicians at conferences and it is a known complication.  Although unlikely to occur in experienced hands, it is a risk that needs to be disclosed and considered.  I have done thousands of injections in over 15 years of practice and have never had this occur in a patient, but do know of numerous cases reported.  There are many more cases of this occurring with inexperienced and nonphysician or nurse injectors.  There is less risk when injecting superficially but greater risk when injecting deep.  One of the techniques I use to try to decrease risk of embolism is to inject lidocaine with epinephrine prior to injection of the filler.  The epinephrine causes vasoconstriction so that the blood vessels are less open therefore more difficult to inject directly into the vessel accidentally.  Fillers like Juvederm and Restylane now contain lidocaine so many practitioners do not inject local anesthesia prior to the filler anymore, and doing the lidocaine with epinephrine prior to filler does have the disadvantage of causing more bruising and swelling and also less precision with correction, but it offers the safety advantage of constricting blood vessels therefore decreasing risk of injecting filler into the blood vessel resulting in embolism.  

To answer your question, the risk is so low that if the injections are preformed by a qualified MD there should be no issue. With that being said, can the risk of an embolism occur with injectables? As we are taught in residency training and medical school, "Never say never!"
The rule of thumb is to have a qualified MD (A boarded Plastic surgeon or Dermatologist).
Slow injection and withdrawal techniques.
A good medical history, especially if use of blood thinners or poor clotting.
If still fearful, do a test area with the injectable. To see the results and effects.
I agree with my colleague, Dr Rohrich, as to areas and differing types of fillers to use. It is best to have choices and recommendations from the treating doctor to which filler might be better for each area.
Hope this helps!