Any time the hero is confronted by a failed saving throw against a death spell, a sleep-murdering assassin, a withering energy drain, an inescapable snare, a hopeless situation or an insurmountable barrier, they may choose to Defy Death. This lucky evasion lets them escape the effects of their calamitous situation, bypass an otherwise unavoidable condition, or get past barriers that would stop them cold, though it dangerously taxes their reserves of luck.
When a PC Defies Death, they suffer one damage die for every level they possess. The first time they dodge doom during a game session, they roll 1d4 for each level. The next time, they roll 1d6, then 1d8, and then 1d10 for each further attempt to dodge their fate. If the damage inflicted by this taxing of their luck would reduce them to 0 hit points, they are instead left at 1 hit point and whatever doom they were trying to slip affects them normally.
It is up to the GM to decide what situations and negative effects can be dodged. When combat is dodged, it usually means the PC has successfully fled an otherwise inescapable situation. When some arcane barrier is overcome by a PC with no access to Dispel magic, it might mean the hero recognizes the ward and knows how to spoil its effect. When a furious mob that has caught the hero in an alleyway is dodged, it might mean some local official is an old friend and rides in to disperse the crowd. The GM is the final arbiter of what can be evaded and the form that evasion takes.