Adding on to what the other commenter mentioned, that is called a breaking change and would generally be avoided at all costs by libssl. See, e.g., the decades-long python3 transition.

I'm also not familiar. But my understanding is that the package maintainers should prevent this situation. Because otherwise even if there are package version dependencies (I don't actually know if pacman does this) it would just block the update which results in a partial update which isn't supported. For example if your theoretical unmaintained Firefox blocks the update of libssl but Python requires new functionality you would be stuck in dependency hell. Leaving this problem to the users just makes this problem worse. So the package maintainers need to sort something out.

It is a huge pain when it happens but tends to be pretty rare in practice. Typically they can just wait for software to update or ship a small patch to fix it. But in the worst case you need to maintain two versions of the common dependency. In lots of distros very common dependencies tend to get different packages for different major version for this reason. For example libfoo1 and libfoo2. Then there can be a period where both are supported while packages slowly move from one to the other.