Yeah, I know what you mean. I wouldn't feel inclined to tell them, if it doesn't affect your ability to do your job then it is really your business. If it is a matter that is important to them they would probably ask you anyway. In general I would keep shtum unless asked directly.
If the bankruptcy is causing you alot of stress and may affect your ability to work then I would "have a quiet word" with your manager so that they are aware what you are going through that way you wont be seen as not interested in the job