Oh my gosh! That screenwriter's car is on fire! Who are you going to call? Probably not their literary agent, at least not until a couple hours after, and then the call will be mostly for emotional support.
Literary agents face no real physical danger as a result of the day to day function of their jobs. Besides braving the Los Angeles traffic daily and maybe a flying stapler (watch out!), agents' lives exist behind a desk, on the phone, and in a conference room, all extremely safe destinations compared to life on an oil rig off the northern Alaskan coast or fighting fires.
Still, the stress from the job can have long and short-term affects. Feelings of anxiety and panic everyday can lead to a whole slew of health problems over time, so whatever happens, remember to relax, exercise, and stick to the latest Hollywood diet trend—well, maybe not for too long.
But really, successfully managing the stress and pressures of the job, and not yelling at your assistant for ten minutes when he forgets to sticky-note the page that mentions your client in Variety, will pay large dividends to your health over the long-run. Play it cool, man.