If this draft passes tech companies "storing and giving access to large amounts of works and other subject-matter uploaded by their users" would be liable for copyrighted content that is shared on their platforms.

They can (but aren't forced to) avoid that liability by making "best efforts to prevent the availability of specific works or other subject matter by implementing effective and proportionate measures, [...], to prevent the availability on its services of the specific works or other subject matter identified by rightholders and for which the rightholders have provided the service with relevant and necessary information for the application of these measures" and "upon notification by rightholders of works or other subject matter, it has acted expeditiously to remove or disable access to these works".

There's also some stuff in there saying these measures should be "effective and proportionate", taking into account how big the company is, how much content is uploaded on their platform and the availability, cost and effectiveness of the measures.