@unnick @CenTdemeern1 Another angle to see this would be set theroy; like a normal d6 would conform to the set {1, 2, 3, 4, 5, 6} while your special die with only one face showing seven would be the set {7}. A true zero-sided set would therefor be the empty set ∅ / {}.
Now we define the action of rolling to picking a random entry of the set... however I'm unsure what this means in the case of ∅:
We could argue that randomly picking is reducing the set to just a set by throwing our all other numbers, this would mean that a d6 would be reduced to {4} (if you roll a 4); in the same manner, rolling ∅ would mean the result still is ∅ since we cant reduce further.
On the other hand we can go the normal way and say it's not reducing the set but producing a number, but numbers themselv can be represented using sets by converting the number (i.e. 3) into a series of nested sets build by their previous components:
0 = ∅
1 = {0} = {∅}
2 = {0,1} = {∅, {∅}}
3 = {0,1,2} = {∅, {∅}, {∅, {∅}}}
(Called Zermelo-Fraenkel set theory)
... so ultemately I think the right answer would be ∅? (I'm not a mathematician, I just like nerdy stuff and happen to know about set theory bc. of uni, but I'm happy to be proven wrong)