I've found a solution of sorts:

subclass Gtk2::CellRendererText, and patch its START_EDITING method to emit the 'edited' signal when the embedded entry receives a 'focus-out-event'.

package Gtk2::CellRendererTextThatIsNotCompletelyUseless;

use Glib::Object::Subclass "Gtk2::CellRendererText";

sub START_EDITING {
    my ($self, $event, $view, $pathstr, $back_rect, $cell_rect, $flags
+) = @_;

    my $entry = shift->SUPER::START_EDITING(@_);

    $entry->signal_connect(
      'focus-out-event' => sub {
         my ( $event_box, $event ) = @_;
         $self->signal_emit( edited => $pathstr,   $entry->get_text() 
+);
         return 0;
      }
   );

    return $entry;
}

1;

[download]

Not elegant, but it appears to work.

I'd also like to nominate the previous reply to this thread to the 2017 Contest of Most Helpful and Well-Considered Forum Replies (and grumble that this place is not what it used to be).

In reply to Re: Gtk2 CellRendererText: how to save the edited value in the cell? by kikuchiyo
in thread Gtk2 CellRendererText: how to save the edited value in the cell? by kikuchiyo

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