In your controller action you have prefixed your Json response with a Data
property:
return Json(new { Data = BreakOut });
So make sure that on the client you are looping on this property:
var items = "";
$.each(data.Data, function (i, item) {
items += "<option value='" + item.Client_ID + "'>" + item.labelname + "</option>";
});
$("#BreakOutValue").html(items);
or if you want to keep your current code then return directly the list:
return Json(BreakOut);
Also I would more than strongly recommend you getting rid of the async: false
parameter in your $.ajax
call. By setting this parameter you are making a blocking request to the server which completely defeats the whole purpose of an AJAX call.