[Cryptography] Signal double-ratchet vs. future breaks in ECC?

[Nemo]

I asked this on the Crypto StackExchange but got no replies:

    https://crypto.stackexchange.com/q/60660/

I understand how a "double ratchet" protects both future and past
messages from one-time key compromise.

My question is what happens if the public key (ECC) algorithm is broken,
while the hash function(s), symmetric algorithm(s), and keys themselves
remain secure. (Consider a hypothetical mathematical breakthrough on
elliptic curves, or quantum computers becoming practical...)

Perhaps somebody here knows the answer or can explain why it is a dumb
question?

Thanks.

 - Nemo