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Singleton Pattern.

The class can contain a static list of the weak-references of all the objects instantiated for the class. Whenever a function which modifies the state is called for an object, the object can call a corresponding static function in the class, which in turn, can call the same function for all the other existing (not garbage collected) objects for that class.

The class could keep its state in static (transient) member variables rather than normal member variables. And the objects would modify this static state. This way, every object has its state synched.

TextBox class can implement Cloneable interface. By default the clone method will do shallow copy of the given object. The "textbox" could be String member of another referenced class.
So, the solution goes like this. Every TextBox class object are cloned to each other. And as cloning provides shallow copy, the same referenced class object is shared amongst all the cloned TextBox class object.

Actually just having the member variables in static is not enough. We need them to be static volatile.

Observer pattern

Observer pattern can address this.