Well, presumably the limit as a force goes to infinity is an unstoppable force, and the limit as a mass goes to infinity is an immovable object. So we can go to the basic form of Newton's law:
F = ma
or, rearranged for our purposes here,
a = F / m
So, clearly we're interested in the limit of a as F and m go to infinity. Clearly, since F and m are both linear with respect to F and m (respectively), their asymptotic growth rates are the same, and thus we can conclude the limit is equal to 1.
Thus, the immovable object experiences an acceleration of 1 m/s^2.
wait, what?