The majority of the companies handle copyright infringement by deactivating or removing the concerned file. But Dropbox is focused on just deactivating the share feature and keeping the file. That is why, given this information users reconsider the reliability of cloud storage services.
Dropbox uses an algorithm creating by cryptographic way a unique id for each file uploaded on Dropbox. Thereby, when a complaint about copyright violation by the user is received, Dropbox stops the sharing of the concerned file.
It’s understandable that users are concerned with Dropbox having access to the content of all files in a private folder. The point of Dropbox is that they respect users’ privacy and that the algorithm locates the file by ID without reading its content.