What makes you think it's a problem returning a big num from the subroutine? There's no evidence of that. Problem: use bignum; isn't in effect in the eval. Fix:

sub operation {
    my ($arg) = @_;
    my $product = eval "use bignum; $arg";
    return  abs $big_number - $product;
}
[download]

Or use the existing bignum instead of making a new one.

sub operation {
    my ($arg) = @_;
    my $product = eval "\$arg";
    return  abs $big_number - $product;
}
[download]