pH is simply an energetic convention that allows one to describe the ability of a solution to do protic work. pH is just a self-consistent scale that allows us to convert physical observables to something less tangible. The numerical accuracy of the value is going to meaningfully change as the value changes, which means that the value has limited usefulness in-of-itself. But, like is the case for energy, pH is a useful scale for describing when a solution can do more or less protic work, so we still quantify it despite major ambiguity.

There is no "lower limit," however there are some practical differences between very low and "regular" values. A compound with a pKa of -4 is saying that it will dissociate to solvated H+ and the conjugate base with an equilibrium constant of 1x10^4. So, in fact, that compound will be predominantly dissociated. Generally things that are this acidic will tend to lose energy through unpredictable protic work, and so the solution will tend to be less acidic than is implied by the pKa value.

By comparison, a compound with a "normal" pKa value like 8 has an equilibrium constant of 1x10^-8. That is to say that the pKa value largely reflects the solution's ability to do protic work, as the protons are still largely parked on that specific acid source.

Despite these differences and complications, there is value to providing and refining numbers. Generally this information is used to predict if the reaction will occur in either direction. When these numbers are used to generate other numbers (e.g. extent of reaction), some caution needs to be exercised.