ALWAYS better to loose a front than a rear:
Loosing a rear means the rear axle cornering stiffness is down by a factor of 2 vs. the front. This means the vehicle will be unstable oversteering regardless of the actions of the driver. Loosing a front means you now have 1/2 the front axle cornering stiffness and the vehicle will be understeering and still be stable regardless of what the driver does. Understeering = stable, oversteering = unstable. When you turn a vehicle at a decent speed, the rear axle actually steps out the opposite direction until the rear wheels generate a balancing sideslip angle to counteract the yaw moment induced by the front axle. With reduced rear lateral stiffness, the rear will NEVER be able to counter the yaw moment and you will spin out. Braking acts the same way on the vehicle. With a rear flat, the soft tire will not balance the yaw moment induced by the good rear tire and the vehicle will tend to spin. With the front in good shape, the front counter steering is most likely to over correct the tendency to turn and the vehicle will spin because it is in an oversteering trim.
The unsteered rear wheels of a vehicle act like the tail on an airplane. Same principle. You need it to dig/stick in order to avoid a 'tailspin'.
All of this is accentuated by a driver attempting to maintain control. Best solution is to do NOTHING, let the vehicle slowly decel, do as little as possible, steering only to stay in the roadway, and NO quick, large, jerky or sudden steer or brake applies. Of you have separate trailer electric brake controls, apply them smoothly to stop quickly. The trailer brake force with a long hitch length will help stabilize your vehicle combination.
There are other readings of your trailering that can help you. A blowout is one special condition. But more often, a tire goes soft slowly. You should evaluate the truck and trailer handling periodicly on long trips by putting small pulse inputs into the steering wheel (I said SMALL, not more than a couple of degrees) and evaluate the truck and trailer reactions. If one starts to get a little oscillatory, stop and check yout loads position (maybe it shifted) and kick a tire. Better yet, measure the pressures. Use a good gauge. Some gauges will let more air out of a tire than should be allowed because they are awkward to use, have leaky parts, and you can't read the numbers. Pencil gauges are the worst for acuracy, legibility and clumsy to use.