Which programming language allows to update any class on-the-fly?

Erlang was designed to support hot code swapping as one of its high availability features.

Objective-C might fit the bill. You can use the functions documented here to add new classes and swap method implementations at runtime, and you can load new NSBundles with additional classes or categories on existing classes if additional implementations are required. GNUStep, while not implementing all of the recent Apple additions to the language, does claim to implement these features (see [1] and [2]).