[dragonwriter]

> What is the responsibility of the ISP to its subscribers in that case?

Largely, to fulfill whatever is in their terms of service, though so long as they follow the counternotice procedures in the DMCA -- which require you first to file a counternotice -- they have no liability to you for removing content in response to a facially valid (even if substantively completely false) DMCA claim, even if they would otherwise under general principles of law or your terms of service (that's why the DMCA notice/counternotice provisions are called "Safe Harbor" provisions -- they provide a shield from existing copyright liability and liability to the user whose hosted content is removed, provided, in the first case, that the notice provisions are adhered to, and, in the second, that the content was removed in response to a DMCA notice and the counternotice provisions are adhered to.)