Current amplification

None current amplification here only resistive DC current attenuation simply current reduction. Current is amplified when at output u have more than is sourced by power source. Passive way is by using transformer for AC and for DC can be done usig an avalanche mode transistors only (or old point contact)

But having more current at the output rather than the power supply means more voltage gets wasted. You cant get more power at the output then at the input

Yes u right if j not couple an active source power gain is imposible. But such device operate directly as step down transformer but have one great advantage whise looks crazy as u see it. It operate o direct coupled DC currents. So if take such transistor and emiter base node polarize with 9 volt battery in same time form output circuit between collector and base with some led without any other power source after turning this on u measure in emiter base inpjt batery circuit a 1 mA and ofcoz at 9 volt yet at output in led circuit u measure 3 volts but also a 3mA a Direct Curent transformer without heat and any switching gizmos.