What is the physical meaning of the empty set? Take the example of rolling one $6$ sided dice. If an event $A$ represents a null set, what would be the outcome or the result of getting the event of an empty set?
For example if $A = \{1,2,7\}$ you can say that $A$ is the set of an outcome of $1, 2,$ or $7$ which the last is impossible. Or $A$ could be the sample space meaning the set of all outcomes, but if $A$ is the null set, does it mean that there are no outcomes, i.e. the dice was not rolled?
I was trying to find independent and not disjoint events for this die example. This led me to consider the null set, but I couldn't visualize what the meaning of the null set was for this scenario.
I think it helps to view events as payoff sets in games. For $A=\{1, 2, 7\}$, for example, we play the game where you roll a $6$-sided die, and I win if it comes up $1, 2$, or $7$.

The empty set, then, corresponds to the "fixed game": you roll a $6$-sided die, and I lose. 

There are other "fixed game" events (that is, events with zero probability): e.g. $\{7\}$. But those are not obviously fixed (maybe one of the faces of the die is marked $7$! Or maybe I can't count very well!), while the empty set corresponds to a game which is fixed by definition.
This is very similar to the physical significance of any number.

I'll use $0$ as an example since it's more interesting from a physical perspective than the others. While certainly, negative numbers have no physical relevance.

If you just say $0$, it has no physical relevance. You can have $0$ chairs, $0$ cars, $0$ snow flakes, etc. But that depends entirely on us to give it meaning, and as long as we don't we can argue (equally validly) that either it has no physical meaning or that it has an infinite number of possible meanings which are not yet determined.

I guess a lot of pure math is like that.

So a null set is not a null set in relation to anything as long as there is no context.

To answer your question specifically, in the case of rolling dice, we could agree that this simply means the dice has not been rolled yet. Though, this interpretation is in no way fundamental or essential.