Reproduction steps:
1. Open attached project "Joysticks TEST"
2. Open scene "JoysticksTestScene"
3. Enter play mode
--- GUI label will tell you the value of Input.GetJoystickNames().Length
4. Connect a controller (I used Xbox 360 and Xbox One controllers)
--- You should see Input.GetJoystickNames().Length increase
5. Disconnect the controller
--- Input.GetJoystickNames().Length stays the same

Code used in the project:
void OnGUI()
{
GUILayout.Label("JOYSTICKS LENGTH:::: "+Input.GetJoystickNames().Length);
}