One more thing as Mr Mbeychok already mentioned about absolute pressure...
There is two understanding to determined the value of pressure as it in absulote pressure and in gauge pressure. the relation between two is :
Absolute pressure = Gauge pressure + 1 atmospheric press
I think this is important as you said on your question term...negative pressure, negative pressure only make sense if we talk about pressure in gauge pressure unit, and the furthest vacuum happen (perfect vacuum like you said if it is can be generate..) should be minus one atmospheric pressure in gauge pressure, which means zero (in any units) in abs zero...