I suspect $_ is being reset by __exhibit_verb_function.

...very likely, as there isn't much else happening in between $_ being valid (in /(\{exhibit\})/) and it having become undefined in pos($_). But unless we get a chance to look at __exhibit_verb_function(), it's hard to tell what exactly is causing it...

Note that many variables like $_ are global unless you localize them, i.e.

!/usr/bin/perl -l
use strict;
use warnings;

sub foo {
    # ...
    $_ = undef;
}

while (<DATA>) {
    chomp;
    if (/^FOO/) {
        foo();
        print "found $_";
    }
    if (/^BAR/) {
        # ...
        print "found $_";
    }
    # ...
}

__DATA__
FOO
BAR
[download]

prints

Use of uninitialized value in concatenation (.) or string at ./828268.
+pl line 14, <DATA> line 1.
found 
Use of uninitialized value in pattern match (m//) at ./828268.pl line 
+16, <DATA> line 1.
found BAR
[download]

While if you write

sub foo {
    # ...
    local $_ = "whatever";
    $_ = undef;
}
[download]

you'll get

found FOO
found BAR
[download]