Very hard to say actually. Depending on the country you live in, something like this may happen. The chances are extremely slim, but they are there. There have been a few lawsuits/cases and one of them ended up with the defendant having to pay over $9.000 per song for 24 songs (about $220.000).
By the way this was for downloads kept in the share folder on Kazaa file sharing program, and the defendant had way more than 24 songs in the share folder.
This is in the US of course. Where else would the government let the record industry dictate what is illegal or not. Also they didn't even have proof that anyone had even downloaded from her. Yes, her. A single mother of two that had enough trouble getting ends to meet even before this.
TG Daily - Single mother loses big in music piracy case