Static doesn’t quite mean “shared by all instances” – it means “not related to a particular instance at all”. In other words, you could get at the static field in class A without ever creating any instances.
As for running two programs within the same JVM – it really depends on exactly what you mean by “running two programs”. The static field is effectively associated with the class object, which is in turn associated with a classloader. So if these two programs use separate classloader instances, you’ll have two independent static variables. If they both use the same classloader, then there’ll only be one so they’ll see each other’s changes.
As for an alternative – there are various options. One is to pass the reference to the “shared” object to the constructor of each object you create which needs it. It will then need to store that reference for later. This can be a bit of a pain and suck up a bit more memory than a static approach, but it does make for easy testability.