Rules as Written, Burrow is undefined in Pathfinder.
The helpful folks at pathfindersrd have the rules for Burrow appended with the following note:
Burrow details were not included in the Pathfinder Roleplaying Game so
the details shown here were copied from d20srd.org.
RAW cannot help you here.
That said, we take the 3.5 rules, as they did:
A creature with a burrow speed can tunnel through dirt, but not
through rock unless the descriptive text says otherwise. Creatures
cannot charge or run while burrowing. Most burrowing creatures do not
leave behind tunnels other creatures can use (either because the
material they tunnel through fills in behind them or because they do
not actually dislocate any material when burrowing); see the
individual creature descriptions for details.
This tells us a few things on its own:
- Burrowing is a form of movement, not a status condition.
- A creature cannot use the Charge or Run actions using burrow movement.
Since burrowing is a form of movement, the condition applied isn't "being burrowed," but rather, "being inside a solid object." Incorporeal creatures have rules for this in Pathfinder:
Enemies have total concealment (50% miss chance) from an incorporeal
creature that is inside an object. In order to see beyond the object
it is in and attack normally, the incorporeal creature must emerge. An
incorporeal creature inside an object has total cover, but when it
attacks a creature outside the object it only has cover, so a creature
outside with a readied action could strike at it as it attacks.
I would give Burrowing creatures the same options. While "burrowed," they
- Can move
- Can use spells, abilities, and items with themselves as the target
- Have total concealment (and total cover) from everything.
- Cannot see outside their burrow - but might be able to make perception checks to hear.
- Can emerge as a free action
While "emerged," a they
- Trigger readied actions from any enemy that readied to attack when they emerged.
- Can attack, cast spells, etc. as normal
- Can see outside their burrow, and be seen as normal.
- Have cover (but not total cover) from everything, and everything has cover from them.
- Can submerge as a free action, even in the same turn as they emerged.
There's nothing I can see that would stop them from grappling someone, pulling them into a burrow, and leaving them there. You may wish to create a house-rule that would allow a creature who gets buried thusly to dig themselves out before they suffocate.