Quirks and Quarks went to one of their Professors of Physics at a noted university and got this totally stupid answer.
 Answer 1. from "noted" university physicist.
     The professor said, "When the tire comes loose, it is in forward torsion from the engine (the rear tire that is) and this released torsion propels the tire ahead of the car. 
Quarks and Quarks announcer ask, "Well what about a front tire or small boat trailer tire that comes off?" "What makes it shoot ahead of the car?"

Answer 2. from "noted" physicist: 
     "When a wheel comes loose of the vehicle the weight is reduced on the tire causing the tire to expand in diameter and hence travel faster than the car."

My question of the professor's number 1. answer: "Why does a rear tire pass the car if the car is in a slowing mode in which there is rear/slowing torsion on the tire. Will it run backwards?"

    My answer to my question. Of course the tire will not run backwards and in the slowing mode it too will pass the car. The small boat trailer tire at the instant of release (it's tangential to the pavement tire to road contact velocity, in the longitudinal plane, is the same as the pulling vehicle's speed), will pass the car for the same reason.

    "Why," you ask? A little physical law involving radial velocity and it's inherent true to the laws of physics, kinetic energy (K2), generated by rotational velocity as well as the car/tire longitudinal energy (K1). Yes the tire has 2 sources of energy, that generated and represented by it's rotational momentum energy, K2, (flywheel kinetic stored energy --  mass x radial velocity squared/2 about the radius of gyration) and K1, energy, as a result of the car's forward speed,  mass x velocity squared/2 in the longitudinal direction -- direction of car travel.
Definitions: In general conversation and writings, the words, "force, momentum, and energy" are used interchangeably and cause much muddying of the waters when discussing these vary different physics  factors.
For my discussions, let's use these definitions that "work" for me in my simple "mechanical" world environment.
    
    Force: The uniform "push" in pounds or kilograms on an object whether it moves or not.
    Impulse: A force in motion (with velocity and direction), vector with direction and quantity, acting on a mass at an instant of time.
    Energy: The capacity for producing an effect and can be classified as stored or transient (in transition).
    Rate of energy conversion: The transition of energy over unit time.
    Kinetic energy: Instantaneous energy quantity of mass in motion. 
    Stored Kinetic energy: Too me, stored kinetic energy is represented by the availability of energy (stored) for later conversion to a desired effect, transitional. "Kinetic" energy and "stored" kinetic energy are represented by the same formula and their values are equal; however, it is this different definition in words that help me understand, sort out, their source and possible multiple effects/actions.
    Momentum: An  impulse represented by a mass in motion, vector quantity, at an instant in time. (Impulse = mv or Momentum = mv.)

    At the instant of release (wheel falls off car), the tire has the same forward velocity as the car plus rotational velocity resulting in different total momentum in absolute amounts (due to different mass and two velocity vectors). The total momentum and resultant kinetic energy of the wheel and car were always different from initial startup.
    Again, momentum or impulse is an instantaneous vector value represented by the formula mv. The tire/wheel also has wheel rotation stored energy (kinetic) that is instantaneously translated to acceleration at the tire/road surface and it shoots ahead of the car until friction energy overcomes stored rotational/radial energy, K2, and K1 forward energy.
    The wheel has mv,  momentum, M1, at release due to rotation plus longitudinal momentum, M2, due to the forward motion/velocity of the vehicle. It is the stored kinetic energy conversion that makes the wheel shoot ahead. Momentum is an instantaneous " vector value" of impulse at release.
     The tire will probably slow rapidly. The car, with much greater mass and resultant kinetic energy, may then pass the tire even when the accelerator is released and the engine is no longer pushing because of it's greater stored energy and perhaps lower friction factors of air and surface friction (assuming brakes where not applied). 
You probably have been to a tire shop that "balances" a tire by spinning it and applying the appropriate weights to the rim. It is easy to visualize the spinning tire flying off the stationary car and hurtling at high speed into the shop wall!! This is an example of rotational kinetic energy being converted to lateral kinetic energy with a resultant different relative velocity --  relative to the building versus the tire spin velocity in relation to the stationary car.
    AS far as the professor's engine torsion force on the rear tire, there is a small added rotational force applied and stored in the "torqued" rubber; actually this source of stored energy is the rubber's internal (molecular) stored energy. This energy is reflected in the drag racer tire that  squats and rotationally twists at acceleration launch. This stored molecular energy is miniscule in comparison with the rotational energy/angular momentum stored in engine, driveline and tires as they are initially spun to maximize engine horsepower at the fastest rate and melt the tire/road surface rubber/asphalt for maximum friction.

   The question of, "Why should a non-driver tire or boat trailer tire speed past the car at release/falling off and the professor's answer of it gaining more diameter and hence more speed with the weight being less at release?" Here again we are talking about a miniscule amount of increase in diameter and possible increase in speed and the ENERGY to propel the slightly larger diameter wheel comes from angular rotational momentum/kinetic energy. A large diameter solid hubcap can fly off the wheel/car and it too will pass the car and it does not EXPAND in diameter.
Just as our studies of the curling rock demonstrate relative to the subjects, momentum and friction, there is often a seemingly untrue and even peculiar outcome. This matter of energy and its conversion to useful work, energy conversion affect our daily lives with sometimes hard to understand results!!