Editar seguindo a resposta por @Amin:
A KLM não tem obrigação de deixar você embarcar com um passaporte vencido.
Por Condições gerais de transporte (ênfase minha)
ARTICLE 9: REFUSAL AND LIMITATION ON CARRIAGE
The Carrier may refuse to transport Passengers and their Baggage, if one or more of the following cases has occurred or is likely to occur:
[...]
(k) The Passenger does not appear to be in possession of valid travel documents, may seek or has
sought to illegally enter a country through which he may be in transit, or for which he does not
have a valid entry document, has destroyed travel documents during the flight, has refused to
allow copies thereof to be made and kept by the Carrier, or the Passenger’s travel documents have
expired, are incomplete in light of the regulations in force, or appear to be fraudulent or otherwise
suspicious (for example: identity theft, forgery or counterfeiting of documents).
[...]
18.2 Travel Documents
[...]
(b) The Carrier reserves the right, in accordance with Article 9, to refuse the Carriage if a
Passenger fails to comply with the applicable laws and regulations, if the Carrier has doubts as to
the validity of the documents presented, or the Passenger does not permit the Carrier to take and
retain copies of any documents or otherwise retain data contained in the relevant documents.
Eu tuitou e a resposta deles foi rápida & claro:
We will only accept passengers travelling with a valid travel document. An expired passport is not valid anymore.
Para estar no lado seguro, sugiro que entre em contato com a embaixada mais próxima e tente obter um novo passaporte ou documento de viagem de emergência.
No entanto, aparentemente, eles podem deixá-lo embarcar a seu critério.