Some interesting mental images there... but when you say:

"The Bentley Subglacial Trench is a vast trench in Antarctica. At 2,555 meters (8,326 ft) below sea level, it is the lowest point on the surface of the earth not covered by ocean, although it is covered by ice. It is similar in size to the nation of Mexico.  [This is huge!  Even if it was not covered by ice, a human could not go down to the very bottom because the vastly increased air pressure would overcome your lungs diaphramic muscle ability to exhale; you would need a deep sea diver's pressure suit to explore this area"

I get confused. Anglogold's Western Deep Levels in South Africa is the world's deepest mine at 12300 ft.I think,  and as far as I know no pressure suits are required to work at its lowest levels...

I think the statement about the breathing is wrong. If you could dig out the ice over the Bentley, the air  pressure would be like what scuba divers breath while 20 feet underwater.  There wouldn't be any problem breathing, though you might get the bends if you departed too quickly after a very long visit.  

I think this trench is cut off from the ocean. It is hard to tell, I could not find any maps that clearly show the topology of the Antarctic land under the ice, but if the ice were gone, the ocean would probably not rush into the Bentley, so it would stay dry. So if a volcanoe were to melt ice there, it should not destabilize anything, just make a lake. There would be no lubricated glaciers quickly sliding off of the Antarctic.

I did find this:
http://usarc.usgs.gov/ant-ogc-viewer/viewer.htm

Hello Everett,

Thxs for responding. Yeah, on second thought, I agree with you that I blew the pressure assumption.  If the caldera was as big as Yellowstone, or similar to previous Antarctic calderas [even bigger than Yellowstone], this could potentially be filling in the trench displacing all that water.  But the big problem would be from the predicted 1500 ft or more of uplift from earthquakes, other volcanoes spouting off, and ejecta melting the main Antarctic ice sheet.  The Western Antarctic Ice Sheet [WAIS] is only good for 20ft of sea-level rise-- the other ice sheet is good for 190 ft-- REAL BIG PROBLEMS for us.

My tutorial was highly speculative-- I bet most real scientists would laugh at the whole shebang sliding off in a short twenty year timeframe-- A 1,000 year gradual process is probably much more likely.  But who knows, Nature can be very surprising.

Bob Shaw in Phx,AZ  Are  Humans Smarter than Yeast?

Somebody is confusing water with air. I seem to remember air is about .03 lb/ft3 at STP, so 8300 ft would add around 2 psi, maybe a little more with compression.
On the plus side, this ice will become a lake that will not empty into the sea.
If it was not covered by ice it would be covered by water - I assume that's the point here?
No pressure suits but they need to blow in lots of refridgerated air to keep the miners cool.  Its hot and the ground swallows up gaps.  Its a hostile environment.