Some years ago I tried my hand at crystal set DXing on HF. Results surprised me. I was even able to envelope detect some SSB amateur signals on 80m.
Broadcast stations from their originating countries (many use relays) were copied including Australia and India. The only power is that from the TX with no batteries or other source of energy at the RX.
See https://sites.google.com/site/g3xbmqrp3/hf/crystalset
See also http://www.arrl.org/files/file/Technology/tis/info/pdf/culter.pdf