Java: Exception thrown in constructor, can my object still be created?

Could you tell me can be some case when exception is throwing in constructor and object is not null. I mean some part of object is created and another is not.Like this

public Test(){
name = "John";
// exception
// init some other data.
}

I understand in this sitiation object Test will be null, but Can be situation that object test cannot be null (delete block of exception not answer :) ) ?