You are not changing the object in the assignment statement, you replace one immutable object with another one. Object String("a") does not change to String("ty"), it gets discarded, and a reference to ty gets written into a in its stead.
In contrast, StringBuffer represents a mutable object. You can do this:
StringBuffer b = new StringBuffer("Hello");
System.out.writeln(b);
b.append(", world!");
System.out.writeln(b);
Here, you did not re-assign b: it still points to the same object, but the content of that object has changed.