What to do if you need to fly in the Schengen area and lose your ID card?

The Schengen system merely aims at removing systematic checks at the border. As discussed in Sufficient Identification for Intra Schengen flights it does not particularly address ID requirements for air travel. It's not even clear that it really entitles you to travel without ID as some countries make it mandatory to carry one in any case and do perform occasional checks.

As I reported in my answer to the earlier question, you might get lucky and be able to fly with other documents but presenting a national ID card or passport still seems to be the norm, certainly at Schiphol. An expired passport, if she has one, would also generally be enough.

Unless you have to fly right now, the best would therefore be to get in contact with the relevant consulate and try to obtain some sort of emergency travel document.

The EU website also suggests as much:

Have you:

• lost your passport or had it stolen?
• realised that your passport has expired during your trip?

In either situation, under EU rules you may travel only with a valid ID card or passport. But help is at hand, as the EU countries have systems in place to deal with such cases.

The conditions and procedures do vary widely from country to country. So if you're in the EU, your first port of call should be your country's consulate or embassy.

Alternatively, she might consider going by train or some other means of overland travel. It does not make it legal or fully guarantees that there will be no ID check but the risks would seem lower and even if there is a control, she could hope to resolve the situation without entirely losing the benefits of her ticket.

Having just been through this myself I can maybe try to exorcise my karma by narrating the events which occurred in the last 24h. For the purpose of this story, I will be a Schengen national currently travelling inside the Schengen area.

T'was the night before my departure that I realised I had lost my ID card. My first though immediately went to the fact that this must have happened to many people in the past, and that if so Travel Stack Exchange would have several answers on the topic. Turns out, most of these advise the traveller-at-loss to contact their embassy/consulate and request an emergency document (ID or passport) for the purpose of returning to their home country. Hence this morning I woke up at some crazy hour with all the best intentions to get a replacement document from my closest consulate, and miserably failed. Let's just say that an ugly combination of train and roadworkers strikes denied me any possibility of reaching the consulate on time before my flight left. I therefore decided to follow @Relaxed experience and attempt to board using my EU driving licence as a form of id. The only difference being of course that I premeditated this, whilst Relaxed did not.

Turns out I was able to board the flight with my EU driving licence as my sole form of ID. In my opinion this was the result of two factors:

1. I was flying back home, i.e. it was the return leg of my trip
2. The check-in staff had mercy (or pity) on me

Of course this is not an actual solution to the problem, but rather a last-resort to try in order to return home from a trip as planned.