I agree with ikegami, the closure variable $int shouldn't change.

Unless this module is messing with internals, the most likely reason is your code snippet is not what you really run

You said

> Naive code:

Could it be you forgot my or maybe $1 is undefined because your if clause does more complicated checks?

Most importantly:

Can you reproduce this problem with exactly the demonstrated code?

Update

Provided this is not an XY Problem.

Something roughly like (untested)...

my $code_ref = eval "sub{ m#INT $int# }" ;
$rule->and($code_ref);
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...will hardcode $int into the sub right away.

But be careful to keep full control of $int and to catch potential eval errors in $@