What happens when power is cheap to the point that you can run an overclocked GPU for a penny a year? That was what the question should have been as it's actually a good question. Does the value of bitcoin drop or does the price of the GPU back it then? And if so, what happens when the CPUs, GPUs and ASICs that "crack" those "passwords" are manufactured for $1 per minirig? What happens to Bitcoin and the network?
Other things become the limiting factors.
Energy may get to the point of being practically "free," but it will never be unlimited.
Suppose we are able to develop 100% efficient solar panels for 1 cent US per 100 square meters? At that point, the limiting factor won't so much be money or electricity as how much space you have to lay out solar panels.
Ditto for "zero point energy" or whatever it's called. What little I know of it suggests it relies on space... 8 cubic meters of space could generate 8x the power of 1 cubic meter of space, but that's it. At that point, the guy with the mansion has the edge on the guy with the tiny apartment. There still wouldn't be an infinite amount of hashing power coming online.
Of course, I'm fairly certain we could probably calculate some actual limit (I believe I've seen some maths on the threads that lean toward that.) There is a minimum energy expenditure per logic/math calculation, and we could probably determine a minimum hardware area/volume required per calculation as well.
Upshot of it all: hashing power will continue to go up, based in part on how much energy out of our productivity we (as a global society) choose to devote to mining. But there IS a hard limit, and there will still only be a new block every 10 minutes on average, and the price per bitcoin will still be primarily determined by demand, and little else.
Q: "What happens to Bitcoin when free energy is available?"
A: Nothing much.