When you write about "blackmail", you are refering to the "Abmahnung" process - essentially a cease-and-desist letter, which can involve lawyers fees, and a contract in which you - if you sign it - pledge to pay a high amount of money if you do go back to your infringing ways. If you do not sign, they will consider suing you.

It is meant to prevent preventable lawsuits (which would be a lot more expensive), but has been weaponised by lawyer firms specialising in copyright enforcement. After a few of these law firms were countersued for inconsistent claims, the law about Abmahnungen was tightened a bit.

I have yet to see an Abmahnung benefitting the GEMA. Law firms usually work for studios.