As Fletch points out, constants are supposed to be, well, constant. Something that varies is called a variable. Perhaps what you want is a subroutine that returns the current value of your variable? This would let you use it like the constant, but without all the weird contortions:

my $foo;

sub FOO () { $foo }

$foo = 1;
print FOO, "\n";

$foo = 2;
print FOO, "\n";
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