Doom Safe is keeping all your skulls inside him safe from shady people. Warning: it can bite.
The difference between Piggy Bank of Doom and Doom Safe is that Doom Safe gives 1,000 which are later multiplied by all skulls' multipliers that a player has, while Piggy Bank of Doom always gives 50,000 each reset.
To clarify, let's take into consideration the following example. A player with nothing but 5 Greed Shards (x32 multiplier) and the Doom Safe, will get after reset 32,000 skulls (the x32 is applied to 1,000 skulls provided by Doom Safe).
The player have to beat Marcus's Challenge during the Bob's Special Day.