The substantive form of alcuno, in other words the pronoun, matches in gender and number with the noun it refers to.
summary
singular
plural
masculine
alcuno
alcuni
feminine
alcuna
alcune
We have a similar problem as the one we had with the adjective forms. The meaning of the plural is clear, alcuni / alcune means some / any. But what is the meaning of the singular forms, alcuno / alcuna. Simplifying we can say that alcuno / alcuna as a pronoun (don't confuse that with the use as an adjective! Used as an adjective it can be used in singular) can' t be used in singular.
One might think that alcuno is used in negative sentences. That's not the case. In this case nessuno is compulsory.
Examples
I haven' t met anybody.
Non ho incontrato nessuno.
wrong: Non ho incontrato alcuno.
That may seem illogical, because the double negation (non ...nessuno) could be understood as positive, but that' s not the case in Italian (and Spanish). Double negation rests negation.
In some isolated cases, mostly in literature, you can find alcuno / alcuna as a postponed pronoun (don't confuse it with alcuno / alcuna used as an adjective => senza raggione alcuna / without any reason), but this use is very seldom.
Example
And all that must happen without anybody coming to know it.
E tutto ciò deve avvenire senza che alcuno lo sappia.
The table below is a simplified summary of all we have said until know.