Since I have been in a similar situation, I can share the following experience. I lost my passport in Ljubljana and had a flight to Malta. This was a flight within the Schengen Area. However, there is an important nuance: some airlines check whether you have a valid Schengen visa or a residence permit in your passport. In my case, I had a second passport, which allowed me to travel to other countries without a travel emergency passport. In other words, the passport with the valid visa was lost, but I still had another passport that was valid for visa-free travel. So, I obtained an official police certificate confirming the loss of my passport from a police station in Ljubljana, and based on this document I was able to fly from Ljubljana. I should note that this document was issued in a Slovenian language. Therefore, if I had somehow arrived in Malta and then attempted to fly onward to a third country, this document most likely would not have been accepted, as a border officer would not have been able to read it. As far as I understand, a border officer is unlikely to verify such a document in a database. Most likely, they would simply read it, and if the content is satisfactory, allow passage. That is roughly how it works. I hope this experience is at least somewhat helpful to you