Well apparently, it is possible to have -5 of something. It's just not clear what enumerating -1 of something is.
So it is possible to have a negative set of elements. The idea displayed in the preceding link is to imagine a bridge linking {• •}, if {• •} has a cardinality of 2, and {•—•} a cardinality of 1, then a bridge, drawn as {o—o} has a cardinality of -1.
I suppose the lazy way of defining an enumeration of -1 would be to just iterate through the elements backwards.
Another possibility, in this
paper, is to define an enumeration of -1 as infinitely looping through all the elements. However, they only define what enumerating -1 elements means on a negative set, showing that it's impossible (in their construction) to have -1 elements enumerated from a positive set. (They define -1 as removal, and removing a positive element works, but removing a negative element keeps it there, looping forever)
Perhaps the third possibility is to just have the idea of a negative enumeration being the addition of elements into the set. This makes more sense from a computer science perspective. But it's not clear what an implementation would look like.
Anyways, interesting, if weird, to consider an enumeration of -1, and I don't believe if it's ever been asked before. Source:
https://math.ucr.edu/home/baez/counting/