package parent;
...

sub AUTOLOAD {
    our $AUTOLOAD;
    return if ( $AUTOLOAD =~ /DESTROY$/ );

    if ( $AUTOLOAD eq 'handled_func' ) {
        # do something
        return;
    }

    $logger->warn("Tried to call $AUTOLOAD.");
}

...

package child {
...

sub AUTOLOAD {
    our $AUTOLOAD;
    return if ( $AUTOLOAD =~ /DESTROY$/ );
    $logger->warn("Tried to call $AUTOLOAD.");
}