The lights are on
Alright, so there's a lot of confusion about how this works. People think that this means Anderson will live if Shepard stops TIM. As far as I know, he will always bleed out and die, without any hint of him still being alive. However, there is a way to prevent him from being shot again by TIM, which I think is what "saving" Anderson refers to. Doing this will unlock more dialogue with him before he passes away. Unfortunately, the trick to this is something most will miss entirely on their first playthrough because of its difficulty (you'll need the right reputation amount each time, so you might miss it).
In order to "save" Anderson, a player must use only Charm or Intimidate choices when the option appears during conversations with TIM, and never deviate (for instance, if you use Charm in your first conversation with TIM, you must only use Charm in the rest of your conversations with him; the same for Intimidate). If you do not do this, then the final option for either choice will remain grayed out during your last conversation with TIM, regardless of how high your reputation is. However, do this, and the option for either choice should appear, allowing you to stop TIM from shooting Anderson and allowing you to speak with him longer than normal.