In the old days, the rules of Magic specified that players' life totals were only checked at the end of a phase, or at the beginning or end of combat. The modern rules, however, specify that life totals are checked as a state-based action, every time a player would receive priority.
This means that by the time somebody's life hits 0, it's too late to play spells or resolve triggered abilities that would save them. The correct play is to take preventative action before the fatal event would occur.
When did this change take place? Was there any specific reason for it, aside from obvious factors like streamlining and consistency?