Renee this is a great question.A BBL is most commonly performed under general anesthesia with traditional endotracheal intubation(a breathing tube), not something like an LMA(laryngeal mask airway). The reason for this is because during the BBL you will go from a supine to prone position and this is the only "safe" airway to move a patient from one position into the next. As for life threatening events, a PE on the table would be an uncommon event unless you have multiple risk factors, a DVT/PE is typically something that comes up days later. A fat embolism could indeed happen on the table and the anesthesiologist/surgeon would know immediately what is going on, if the procedure was not being performed in a hospital setting you would be rapidly transferred to a hospital. I hope this answers your questions, a properly performed BBL is a safe procedure. Good luck.