Laravel Checkbox returns always true in live search

I have a problem with a checkbox: when doing a LIVEsearch, the value of the checkbox is always set to 1/true. When i do the same thing in a normal search (without the js file) i dont have this problem. First of all the code of my checkbox:

Than the Code of my javascript (i guess the problem is to get the value of the checkbox)

<script>
$(document).ready(function(){
   $(".search").keyup(function(){
       var staffid=  $("#search-staffid").val();
       var firstName=  $("#search-first-name").val();
       var lastName=  $("#search-last-name").val();
       var birthday=  $("#search-birthday").val();
       var children=  $("#search-children").val();
       var deleted=  $("#search-deleted").val();
       if(staffid == "" && firstName == "" && lastName == "" && birthday == "" && children == "" ) {
               $( "#liveResult" ).html("<b>Suchergebnisse werden hier angezeigt</b>");
       }else {
               $.get( "" +
                    '?staffid=' + staffid +
                    '&first_name=' + firstName +
                    '&last_name=' + lastName +
                    '&birthday=' + birthday +
                    '&children=' + children +
                    '&deleted=' + deleted
                , function( data ) {
                   $( "#liveResult" ).html( data );
            });
       }
   });
});
</script>

As you see i have some other fields, they work without any problems. Finally the Code of my controller:

public function liveSearch(Request $request)
{
    $data = [
        'id'            =>  $request->staffid,
        'first_name'    =>  $request->first_name,
        'last_name'     =>  $request->last_name,
        // converts date format only if birthday != null
        'birthday'      =>  ($request->birthday ? date('Y-m-d', strtotime($request->birthday)) : null),
        'children'      =>  $request->children,
        'deleted'       =>  $request->deleted
    ];

    if (is_null($data['id']) && is_null($data['first_name']) && is_null($data['last_name']) && is_null($data['birthday']) && is_null($data['children']))
    {
       return view('staff.livesearch');
    }

    else
    {
        dd ($data['deleted']);
    }
}