A copyright holder may file a takedown notice [1] against a platform that hosts a link to copyright-infringing material like a book from Library Genesis or an article from sci-hub. Failure to act upon a legitimate takedown notice opens the platform operator up to a civil law suit. The platform does not have to take proactive measures to prevent infringing links from being posted by users. Some platforms like YouTube take more aggressive measures to proactively guard against infringement, but they are not required by the provisions of the DMCA.

[1] https://guides.dml.georgetown.edu/c.php?g=904530&p=6510951 (See "Notifications of Claimed Infringement")