Hydraulic brake cable invisible leak. Possible? I've crashed hard, handlebar rotated as much as it could and I guess rear brake cable was stretched. Braking became soft. Time to bleed I thought.

But I'm completely unable to bleed it. Tried some many times w/o any success.

To test my bleeding techniques I've rebleed other (front) brakes - everything is fine. Even tried to push air first and then fix it by rebleeding. Works perfect.

Then I've tried to move parts of working brakes to non-working brakes and bleeding each time. Turned out that the fail point is cable (hose).

However I don't see any leaks or damages. At all. 

Brakes: Avid Elixir 3 and it uses DOT fluid.

Is that possible for the cable to have some sort of invisible internal leak?
Generally speaking it is possible. But you should also make sure that the pistons on the rear caliper are not pushed out too much which could lead to possible oil leak, usually but not necessary when the brake pads are too worn (say less then 0.5mm). I had lots of leaking problems with one of the Shimano brakes in the past, and like you I couldn't identity the problem.

You could start by replacing the brake hose with the new one, which should help narrow the problem. Other than that the canister cap on the brake lever knows to give problems sometimes. Make sure the cap is well tucked in in the right place, also don't forget that there is usually a small piece of thin rubber between the canister cap and the lever which also stops oil going out. One more major thing that can also go wrong with the lever is the small piston below the thing you actually press to brake. One piston pushes the oil from the lever, and the other two pistons (or four in same cases) push the brake pads.

Maybe the best way the determine where oil leaks is to fill the system with new oil, push out the air if there is any and leave it a couple of days to sit like that, but also wrap some toilet paper tight around places that could possibly leak oil, around both hose ends, canister lever and piston and caliper and inspect the t.paper every couple of hours for oil marks. It may sound silly but can actually help.