I'll say it differently. Can you have negative life or you can't have less than zero life? That was the original intention, but you didn't quite get it, because I know you have to keep track of life.
Your original post lacked a question mark, which can be confusing. Please try to type more carefully.
Yes, you can go into negative life totals and must keep track of this.
And I think this thread has gone as far as it can.