jQuery Success or Fail response help needed.

Is there a reason you're using print_r? If you want to inspect it yourself you can use a JSON prettyify formatter argument like (PHP 5.4+): json_encode( $output, JSON_PRETTY_PRINT ). Using print_r is going to invalidate the JSON to any API, but I suspect you're just investigating the results yourself. Consider grabbing one of the many JSON extensions for browsers that automatically allows you to receive and view JSON data in a pretty way instead and work directly with the JSON.

That aside, I always like to send a status on any API endpoints that return data with a predefined set of messages I'll understand on the other end. Every JSON object I send back has a "status" (int), "message" (helpful human info) and/or the "results". That way I'm comparing against a bunch of useful possible "status" that will let me debug the client side much easier.

e.g. Success (code 1):

{
    "status": "1",
    "message": "success",
    "results": [
          {
              "First": "John",
              "Last": "Doe",
              ...
          },
          ...
    ]
}

I tend to make the status codes constants defined in a global config or modular to the part of the app I'm making, depends on the situation. Either a class for constants or just defining them with regular variables like $_ERROR_NO_RESULTS = -1; so, e.g.:

// response codes
$_ERROR_NO_RESULTS = -1;
// (or bundle)
$_ERROR_NO_RESULTS (object) array( 'status' => -1, 'message' => "error: no results" ) ; 
// then later (bundle is easiest) 
$response = $_ERROR_NO_RESULTS; 
echo json_encode( $response, JSON_PRETTY_PRINT );

No results isn't always an error but if you were expecting some then it just may be.

Over time and as any application grows it should be a centralized thing but making a status has helped me assign a ton of useful errors so I rarely need to look at the PHP, the codes let me know exactly what's going on for each response. Much easier to test against as well.

In your else block:

$output = 'No results found';

In your jQuery, check whether the response == 'No results found'. If it is, display that. Otherwise, process the results as normal.