I haven't searched every iteration of the phrasing or words involved, so I'm not sure this is all the relevant info in the book, but here's what I've found:
page 17 mentions "If you're one of the Awakened, then technology joined to your body disrupts the flow of mana. The more 'ware you have, the weaker your connection to magic"
page 38 says "not all characters have this attribute; it is only for magic-using characters..." but that doesn't exactly mean that having Magic 0 is the same as not having the Magic attribute.
page 228 covers critters that lose essence and how they die at 0 essence
page 224 covers that a character drained to 0 essence by an essence draining critter dies
and the only instances of "burn out" in the book are both on the (hilariously terrible) glitch suggestions table
That said, my experience with this game has lead me to believe that pretty much no player ever is going to play a magical character and deliberately reduce their magic rating to 0 - so the most likely cause of a character hitting 0 magic is by hitting 0 essence because of essence drain, and that still specifies death so there aren't any unanswered questions in practical scenarios.