What will happen to existing cyphertext when today's encryption is broken?
For me it is absolutely not certain at all that many cryptographic primitives will become broken. This was certainly true - to some extend - for older algorithms. But modern cryptography is a different beast than the classical ciphers. We know a lot more about various attack vectors and semantic security. So your initial premise is very speculative.

Symmetric algorithms are already thought to be relative secure against quantum analysis, only halving the key strength (in bits) at best. There are a lot of asymmetric primitives that could be broken using a full fledged quantum computer, but there are certainly post quantum algorithms available. They may not be completely stable or standardized yet, but they are there.

Now you start to talk of an "event" that would happen in the future. Now I speculate that this "event" will never happen. Even if the algorithms we use today get broken, they won't get broken all at once. There are different levels of being "broken" as well, even MD5 - a known broken hash - is still secure in many protocols (password hashing, key derivation, HMAC, you name it).

If ciphertext gets broken it will not happen all at once either. And the impact of the plaintext becoming available will depend completely on the contents of the plaintext. This could be huge for state secrets. However, for the majority of the plaintext: the ciphertext will either not be available to persons that want to abuse the information or the plaintext will have completely lost the importance it once had.

Huge data leaks are happening right now, and the world moves on. We don't need any magic cryptographic breakthrough for that. If you want to know the impact you only need to study what is happening today.