See trembling hand equilibrium.

A trembling hand perfect equilibrium is an equilibrium that takes the possibility of off-the-equilibrium play into account by assuming that the players, through a "slip of the hand" or tremble, may choose unintended strategies, albeit with negligible probability.

First we define a perturbed game. A perturbed game is a copy of a base game, with the restriction that only totally mixed strategies are allowed to be played. A totally mixed strategy is a mixed strategy where every pure strategy is played with non-zero probability. This is the "trembling hands" of the players; they sometimes play a different strategy than the one they intended to play. Then we define a strategy set S (in a base game) as being trembling hand perfect if there is a sequence of perturbed games that converge to the base game in which there is a series of Nash equilibria that converge to S.

One possible interpretation of "if I always cooperate, what would happen if I don't" is "what is the limit, as X approaches 1, of 'if I cooperate with probability X, what would happen if I don't'?"

This doesn't reasonably map onto the 1=2 example.

"1 is not equal 2, but what if it were?" = what if I could travel faster than the speed of light.

Off the equilibrium path = what if I were to burn a dollar.

Or things I can't do vs things I don't want to do.