The following isn't JSON:

{"abc":"abc\'abc"}
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What are you trying to do? You might be trying to generate a JavaScript string literal from JSON, but then you'd want something like the following.

'{"abc":"abc\'abc"}'
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If that's what you want, you can use the following:

{
    my %translations = (
        "\r" => "\\r",
        "\n" => "\\n",
        "'"  => "\\'",
        "\\" => "\\\\",
    );
    
    my $meta_chars_class = join '', map quotemeta, keys %translations;
    my $meta_chars_re = qr/([$meta_chars_class])/;
    
    sub text_to_jslit {
        my $text = shift;
        $text =~ s/$meta_chars_re/$translations{$1}/g;
        return "'$text'";
    }
}
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As a Template-Toolkit plugin:

package Template::Plugin::JavaScriptLiteral;

use strict;
use warnings;

use Template::Plugin::Filter qw( );

our @ISA = 'Template::Plugin::Filter';

my %translations = (
    "\r" => "\\r",
    "\n" => "\\n",
    "'"  => "\\'",
    "\\" => "\\\\",
);
    
my $meta_chars_class = join '', map quotemeta, keys %translations;
my $meta_chars_re = qr/([$meta_chars_class])/;
    
sub init {
    my $self = shift;
    $self->install_filter('jslit');
    return $self;
}

sub filter {
    my ($self, $text) = @_;
    $text =~ s/$meta_chars_re/$translations{$1}/g;
    return "'$text'";
}

1;
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For example,

// PARAMS: { data => { abc => "abc'abc" } }

[% USE JSON %]
[% USE JavaScriptLiteral %]
var json = [% data | json | jslit %];
alert(json);  // {"abc":"abc'abc"}
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However, one usually wants to assign the JSON to a JS var, not a string representation of it.

// PARAMS: { data => { abc => "abc'abc" } }

[% USE JSON %]
var data = [% data | json %];
alert(data.abc);  // abc'abc
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