Would a parser know if input String contains incomplete syntax?

Suppose we have the following BNF Syntax for input string:

<Directory> ::= <file><blank>

<file> ::= <alpha><alphanumeric {0..8}>

<blank> ::= 'b'

and I want to test the following condition: file doesn't have alpha with the following input string: "abc7eb".

Would the parser (LL) discriminate that "abc7e" belongs to <alphanumeric>? and that <alpha> is not exist in this string? or will consider "a" as <alpha> and "bc7eb" as <alphanumeric>? if this is the case how can I generate a test input for my condition?