An employer doesn’t need to know you’ve filed for bankruptcy

A Globe and Mail article addresses these questions: If I've filed for bankruptcy, do I have to disclose this to a prospective employer? Could they legally do a search that would let them find that out? Does this limit my career choices? Will I be unable to get a job where I handle money (banking, real estate)? How might this fact limit me in my job search? Is there anything I can do to mitigate this fact?