There is this popular rpg maker horror game that has this gameplay mechanic and it actually works in that game, for an rpg it would be very frustrating of course. Forgot the name of the game though. Anyway, it certainly is a mechanic you have to be very careful with.There is no default way of deleting a save file. You will need a plugin.
Moving to JS Plugin Requests
I would not play a game that deleted your saves whenever you failed. There is no joy in having to start over just because you failed a battle.
If he wants something like that, it's easy to acomplish...Yeah, it would have to be a very specific kind of game, with a very good reason for the deletion.
This wouldn't stop someone making multiple saves just in case they lost a game. Unless you removed the save option as well, or only let them have one save file.