So you could implement a chip which reacts like an official passport. When the border guards see that the signature is invalid, you can explain how it's just a prank and you'll all have a jolly good laugh about it.

There are also optional subprotocols that allow the chip to be authenticated (i.e. proof it knows a private key). These prevent copying valid signed data to a different chip.

But you could achieve much the same effect with a hammer.

I've seen crashes in PKCS#11 drivers when reading cards with malformed data. So, the possibility, in theory, is always there.

Source: I have been working on a blockchain implementation in the past that was compatible with the cryptographic functions in an NFC passport. Basically using a standard NFC passport as a cold wallet.

Fun fact. The cryptographic system even differs per country.

E.g. the Dutch don't trust the NIST elliptic curves so use the brainpool curves instead. Some other countries are still using RSA iirc.