I have temporarily lost my Dutch passport. I'm on a round trip from the UK to Germany. I have confirmed my passport has been found and it's safe with Lost Property at Bruxelles-Midi station, where I will pick it up as I pass through on my way home in two days (the same lost bag contains all my other forms of ID, which are safe as well). I'm currently in Germany. I have a copy of my passport but no other form of identification. Is there any requirement on me to notify any authorities, or do I just carry my copy around hoping that the copy + the story will do should there be situations where I am asked to prove my identity? Due to work obligations it would be difficult for me to travel back and forth to Brussels before I am due to return anyway.
Under German law (§ 8 FreizügG/EU) you are required to have identity papers and to carry them with you during the border crossing. Failure to do so would be a misdemeanor (§ 10 FreizügG/EU) if it was intentional or negligent and may be punished by a fine. I seriously doubt that a couple of days more or less would make a difference, and going to Bruxelles now would almost certainly be more expensive than the fine. (I agree with the comment by Coke that such a fine is unlikely, but the law is on the books.)
As I understand it, as an EU citizen you are not required to carry the passport with you at all times, but having no document might complicate things if it should be necessary to confirm your identity, e.g. if you get involved in a traffic accident.
You might check if there is a Dutch consulate nearby and if they can issue an emergency passport.
You can travel freely in the EU without a passport, it is however in some countries required that you can identify yourself. In this case I would advise that you just travel back to Bruxelles and collect your passport there a copy would suffice for a random ID check on the streets.
Remember that there need to be an event or situation that would require you to identify yourself as at random it is not allowed in most countries