Super Simple Death Save for Dungeons & Dragons

 This is an old-school take and most likely not relevant to 5e of the worlds most popular board game. But for your OSR game it fits the tropes of early play. Also, someone has probably already thought of this and has put it out there. I just haven't seen it yet. 

When the PC reaches zero Hit Points, instead of death they may choose to reduce their Hit Die to the next smaller die size. Only have a d4 Hit Die? To bad, no death save for you.

This means Magic-User and Thief class do not get a death save, they follow the standard zero Hit Points and you are dead. Outside of the Fighter, all other classes have a d6 Hit Die, so these classes get to cheat death once. With the Fighter having a d8 Hit Die they get to save from death twice. 

It should be noted the save is automatic, there is no roll to make. And just to be clear, this does mean, moving forward, the PC rolls this new lower die for all additional levels reached.