For lexical variables, you may be able to do something with Lexical::Persistence.

#!perl

use warnings;
use strict;

use Lexical::Persistence;

# Create a new dynamic closure.
my $dc = Lexical::Persistence->new();

# Prime a variable with a value.
$dc->set_context( _ => { '$cat' => "persistent" } );

# Call a function within it.
$dc->call(\&function);
exit;

sub function {
  # $cat is already initialized.
  print "persistent cat is '", my($cat), "'\n";
}
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