Learn Spanish (Latin America): Si no hay un bolígrafo en el estuche, puedes usar cualquiera. - If there is not a ballpoint pen in the pencil case, you can use any one.

In this sentence, cualquiera is acting as a pronoun meaning 'any one' (referring back to the pen). You only drop the final 'a' to make it cualquier when it comes directly before a singular noun, like in the phrase cualquier bolígrafo (any pen).

Since bolígrafo is a masculine noun, shouldn't cualquiera change to match its gender?

No, cualquiera is a unique word that doesn't change its ending to match gender. Whether it replaces a masculine noun like bolígrafo or a feminine noun, it always stays cualquiera.

Why use no hay instead of no está here?

We use hay (there is / there are) to talk about the general existence of things. Since we are stating whether a pen exists inside the pencil case, we use no hay un bolígrafo. You would use no está if you were talking about the location of a specific, already-known pen (for example, el bolígrafo no está en el estuche meaning 'the pen is not in the pencil case').

Is bolígrafo the most common word for 'pen' in Latin America?