Every now and then, ideas like 'nullar number' or 'indefinite number' make the rounds in the conlanging sphere of the internet. Since I am not about simple solutions, I am not going to leave it at that, though.
Nullar numbers seems to me to be an obvious candidate for defective paradigms. It seems unlikely to me that every form a singular or plural noun can take would also exist for the nullar, in case the language has even a moderately rich morphology.
Nullar is apparently not attested in any language, afaik, and this of course opens up for some speculation: it seems to me that nullar would maybe follow a slightly modified accessibility hierarchy, where objects (or even absolutives) are more likely to have nullar forms than (transitive) subjects, and beyond that, transitive subjects followed by some kind of instrumental or comitative and only then datives and other obliques?
The justification for this would be that an instrumental or comitative nullar basically is not all that far from an abessive, and thus this is likely to be a fairly common use of the nullar - clearly the abessive/privative is sufficiently useful to exist, which kind of indicates something about the way we talk about absences.
On the topic of indefinite numbers, though, first we need to specify a bit more clearly what I mean. Plurals tend to be somewhat indefinite in that we generally do not automatically specify the number of members of a plural referent. What I know mean, though, is a referent where number is entirely unspecified, i.e. it can be any of the available numbers in the language.
This, again, feels like a number that would likely have a defective paradigm, but beyond that, it feels like a number whose marking even would be defective in some sense - maybe lack of plural congruence on adjectives and verbs? Maybe only partial application of plural marking (i.e. suffixes, but not umlaut, in languages where plural is formed by application of both to some nouns), maybe failure to apply gender marking?