package whatever;

my %customDestroy;

sub new {
    my( $class, $flag, ... ) = @_;
    my $self = {};
    ...
    $customDestroy{ $self } = 1 if $flag;
    return bless $self, $slass;
}

...

sub DESTROY {
    my $self = shift;
    if( $customDestroy{ $self } ) {
        ## special behaviour
    }
    else {
        ## normal behaviour
    }
}