Is there an official rule about this? I googled and found nothing (only oppinions, but no one seemed to know for sure...)
Can your threat level be negative?
This is covered in the FAQ, no value can be reduced below 0:
"(1.43) Modifiers of variable quantities
The game state constantly checks and (if necessary)
updates the count of any variable quantity that is being
modified. Any time a new modifier is applied, the
entire quantity is recalculated, considering all active
modifiers.
A quantity cannot be reduced below zero: a card cannot
have “negative” cost, stats, keywords, etc."
Also, the threat level is specifically addressed in latest 1.8 FAQ (the very last item on page 15):
Q: Can a player’s threat be reduced below 0?
A: No. The threat dial does not allow negative values.