The bulging taxbag is an item that is unobtainable via normal gameplay. During The Fremennik Isles, in the part of the quest where players collect taxes for King Gjuki Sorvott IV, the tax bag becomes bulging when they collect at least 33,000 coins in taxes from the citizens of Jatizso. However, players can only collect a maximum of 29,000 coins in taxes, resulting in a hefty tax bag.
For the tax bag to become bulging, players must perform an exploit:
Destroy the tax bag, and filling the inventory entirely.
Attempt to collect taxes from Vanligga Gastfrihet, and offer to pay her taxes with your own coins. As you have no space in your inventory, a tax bag is placed in your bank containing the taxes you paid for her.
As the flag that tracks whether Vanligga's taxes has been paid or not is not set when paying her taxes in this manner, players can keep paying her taxes until the tax bag in the bank is bulging.
Trivia
Unlike the obtainable tax bag items, it is spelt "taxbag" and has a "check taxes" left-click option instead of "check tax".