It really depends ! The Casey Anthony bankruptcy case and state court lawsuits against her provide an insight.
For almost all situations, a temporary hold, or Stay, is put in place when you file bankruptcy of any type which prevents any court suit from continuing immediately.
If you are filing bankruptcy, and surrendering real estate, foreclosures against that real estate can start or continue when relief from the stay is granted by the bankruptcy judge.
If you are filing bankruptcy and have other types of law suits pending against you, it may be possible for that lawsuit to continue after relief from stay is granted, to see what type of judgment or award is entered. There are specific types of judgments or awards that can not be discharged, or wiped out, in bankruptcy. This appears to be what is happening in the Casey Anthony bankruptcy. Her lawyers seem to be arguing against allowing the state court lawsuits against her to continue.
Always be certain to share with your attorney information about ALL lawsuits that you are a part of when you file bankruptcy or even that arise during your bankruptcy.
UPDATE, 6-28-13: The Bankruptcy Judge in Casey Anthony’s bankruptcy case has ruled that the tort claims against her be tried in Federal Court in front of a jury. Link to a news article on the story, click here