my $mw = 'MainWindow'->new;
$mw->GUIask->pack;

MainLoop();
[download]

When I click on the red button, the frame disappears. I don't get any errors.

Please provide more details.

Here is the latest copy of the code, and a driver-program

$Tk::GUIask::VERSION = '1.0' ;

package Tk::GUIask;

use strict;                      # https://perlmonks.org/?node_id=1111
+8320
use warnings;                    # my first pTk-MEGAWIDGET: I develope
+d the code. It was widgetized by a "perl monk"
use Tk;                          # THIS THING WORKS!!

use base qw/ Tk::Frame /;        # Frame-based composite
use List::Util qw( first );

Construct Tk::Widget 'GUIask'; # install MyNewWidget in pTk namespace

{ # for package


# sub ClassInit                    # called once to initialize new cla
+ss
#   {
#     my($class, $mw) = @_;
#     $class->SUPER::ClassInit($mw);
#   }

sub Populate                     # called to build each widget instanc
+e
  {
    my($self, $args) = @_;
    $self->SUPER::Populate($args);
    my $search = '';

    my $frame = $self->Frame(
                             -borderwidth => 5, -relief => 'ridge',
                            )->pack(-fill=> 'both', -expand=> 1);

  my $label = $frame->Label(
                             -fg => 'blue', 
                             #-font => 30,
                           )->pack(-fill => 'x');

my $lbox;
    
  # my $lbox = $frame->Scrolled(
  #                              Listbox => -scrollbars => 'se',
  #                                         -height => 20,
  #                                         -selectforeground => 'oran
+ge',
  #                                         -selectbackground => 'stee
+lblue4',
  #                                         -exportselection => 0,
  #                            )->pack(-side => 'bottom', -fill => 'bo
+th', -expand=> 1);
  my $entered;
  my $entry = $frame->Entry(
                              -textvariable => \$entered,
                             # -validate => 'key',
                             # -validatecommand => sub
                             #                         {
                             #                           my ($want) = 
+@_;
                             #                           length $want 
+or return 1;
                             #                           my @list = $l
+box->get(0 , "end");
                             #                           my $item = fi
+rst { $list[$_] =~ /^\Q$want\E/ } 0 .. $#list;
                             #                           defined $item
+ or return 0;
                             #                           $lbox->select
+ionClear( 0 , "end"  );
                             #                           $lbox->select
+ionSet($item);
                             #                           $lbox->see($i
+tem);
                             #                           1 # to allow
                             #                          },
                          #1;
 
                          )->pack(-fill => 'x');



    my $button = $frame -> Button(
                  -text => "Abort",
                  -bg => 'red',
                  -command => sub {
                                   
                                  ($frame -> destroy() ) if Tk::Exists
+($self );
                                  }

                            ) ->pack(-fill => 'x' );

  $self->ConfigSpecs( DEFAULT => [$lbox], text => [$label] );

  $self->Delegates( Construct => $lbox, insert => $lbox );
  }

1;
 
} # end package




###############################################



#! /usr/pkg/bin/perl


##  GOAL: write a simple pTk program for testing 
##  custom MEGA-WIDGETS

############################################################

# use strict;

 use warnings;        ## These 2 lines give useful debug-info
# use diagnostics;    ## COMMENT when done debugging...

use lib ("/home/tgruhn/PTK-MEGAWIDGETS"  );
#  use lib ("/usr/local/MEGAWIDGETS"  ); ## ALTERNATE dir; to test 
                                      ## MEGAWIDGETS library


use Tk;
use ListBox3; 
use GUIask;


############################################################

my $top = MainWindow->new(); ## MUST  be specified as 'our ($top)' abo
+ve

############################################################

############################################################


 # my $listbox = $top -> ListBox3;

 #    $listbox -> pack();

 #    $top -> Button (
 #                     -text  => "Abort" ,
 #                     -bg    => 'red' ,
 #                     -command => sub { ( $top -> destroy() ) if Tk::
+Exists( $top ) ; }

 #                   )-> pack ( -side => 'bottom' , -fill => 'x' );


############################################################

############################################################

my $GA = "ENTER A FILENAME:  ";

my $GUIask = $top -> GUIask(
                -text => $GA,
               );
   $GUIask -> pack();


    $top -> Button (
                     -text  => "Abort" ,   ## THIS BLOCK ALSO WORKS!!
                     -bg    => 'red' ,     ## but what if I want it in
+side the 'GUIask' widget?
                     -command => sub { ( $top -> destroy() ) if Tk::Ex
+ists( $top ) ; }

                   )-> pack ( -side => 'bottom' , -fill => 'x' );






MainLoop();
[download]

Right before 'MainLoop' I have a call to 'Button'. THAT WORKS -- but I want it inside of the megawidget (GUIask.pm) . If I click on 'Abort' then kill widget and make another choice from the main menu. I also wanna be able to change $GA since this will be used in different situations where user input is desired.

In your original code, you had the button code in the megawidget, but commented out. I uncommented it and it worked. Please post code we can run to see the problem without having to shuffle parts of it around and guessing.
map{substr$_->[0],$_->[1]||0,1}[\*||{},3],[[]],[ref qr-1,-,-1],[{}],[sub{}^*ARGV,3]