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Would liquid pool up as you melt the ice? I guess you'd need to pump it out. Is that even possible at that depth? The liquid might boil on the way up.

Your craft is denser than the liquid, so you just kinda drop through it and keep melting.

Doesn't the heat you have to produce increase as you go deeper?

In this case, the digging is from the perspective of a Europan living under the ice, and having to dig to go up.

Of course, barring collapse, the rocks won’t reform right above you as you go.

I wonder if one can apply some heat to the cable or wire dropping you down, and thus create a more open conduit.