If you have control over the first object, you can use Class::Observable:

package FirstObject;

use base qw( Class::Observable );

...

sub DESTROY {
    my ( $self ) = @_;
    $self->notify_observers( 'DESTROY' );
}

package SecondObject;

sub take_first_object {
    my ( $class, $first_object ) = @_;
    $first_object->add_observer( $class );
}

sub update {
    my ( $class, $first_object, $type ) = @_;
    return unless ( $type eq 'DESTROY' );
    ... do stuff with $first_object ...
}
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If you don't have control over the first object and it's well designed, maybe you could subclass it to add the Observable behavior.

Chris
M-x auto-bs-mode