The Extinction Bank is a miscellaneous item that can be dropped from various sources and may be given as rewards by other means, like the Otherworld Tower dungeon.
The Extinction Bank should not be seen as a monster drop as of the Otherworld Update, since it is not listed on the Itempedia.
It is considered to be an exceedingly rare drop from creatures that roams in the Frontier, like the Esteemed Gumbo and Primeval Genie.
It is sold at a selling price of 5,000,000 gold after interacting with Big Box or Little Chelli. It do not have any usages that would benefit the player, other than for gold profit.
One rumor includes that the Extinction Bank could have some sort of connections with Red Ratboy, an NPC that can be found on the leaves of a pine tree in the Ancient Forest, upside-down. Red Ratboy could have been the 'teller' in the Extinction Bank's description, and hence why the Red Ratboy appears to had leaped into the air and ended up staying in the particular spot players can now see.