Can FPDI import encrypted/protected PDF documents?
FPDI does not support importing of encrytped PDF documents. After all this makes no sense, because the resulting document is a completely new document which may be re-encrypted or not.
Encrypting a resulting document is possible with the FpdiProtection class, which is an enhanced version of the FPDF_Protection class from the script repository of FPDF.
If you receive an error message like "This PDF document is encrypted and cannot be processed with FPDI.", you tried to process an encrypted PDF. If you can open this document without entering a password in your PDF viewer the document is encrypted without a user-password. That doesn't mean that the document itself isn't encrypted but that the decryption process simply works with an empty password. Anyway FPDI cannot process this document.
If you need to modify an existing document, that is already encrypted you may checkout any SetaPDF product.