In a very similar way to diving, you could tunnel into soil and move about out of harms way. Probably one or two very specific tiles it can be done on for ease of dungeon design.
Can travel under blocks placed on top of special soil, allowing ways to block paths that allow only this tunneling mechanic to pass.
Can be used for combat, emerging from the ground under an enemy will attack them and knock them back.
Maybe some special underground enemies or traps you can't attack that will chase you when you burrow?
Potentially some special interactions with Shovel, as it is a fellow digging item.
Some or all items that are in diggable holes could block a burrowing players movement.
In addition to digging items up, items could potentially be buried by a shovel to move them underground. This could block underground enemies and traps, and maybe other effects depending on what is buried.
Additionally, maybe players with the burrowing item can jump into holes to enter the underground layer. If the hole isn't on burrowing terrain they can't go anywhere, but if its on special soil they can burrow like normal. The point of this addition is the possibility of special soil types, for example one where you can move but you can't enter or leave it because it's too hard. You could place holes over these tiles as an entrance and exit.
That is a lot text where I rambled on. TLDR: Underground Mechanics, Special Tile and Burrowing Item allowing movement underground. Special interactions with the Shovel and its diggable holes.