In theory, nothing could go wrong using this simple crystal set from 60 years ago, from the February 1956 issue of Popular Electronics. As the photo makes obvious, it’s a simple crystal set that uses the house wiring as an antenna. It has no tuned circuit, so it simply pulls in the strongest local station.
The circuit is isolated from the line by a .01 uF disc capacitor. A disc ceramic rarely fails, but one failure mode is a dead short. The article warns “do not omit the blocking capacitor under any circumstances.” It also points out that all of the internal wiring should be taped over or covered with spaghetti tubing. Only one blade of the plug is used, so presumably, even if the capacitor shorts out, there’s no immediate risk of electrocution.
But just to be on the safe side, the article also warns that you should “observe the same precautions in using this crystal receiver as when using the common a.c./d.c. household table radio. Don’t hold it while standing on damp basement floors, handling water faucets or gas stoves, or when taking a bath.”
Of course, if you’re using this set in an emergency when the power is out, I guess you’re OK. But you still want to observe all of these precautions, because eventually the power will be back on.