This would be the closest translation where the reader is an American. Such an application is one made by a debtor (or his or her creditors) to a court to declare the debtor bankrupt. Upon court's approval, the debtor's assets are typically sold off (liquidated), in a Chapter 7 case, and the proceeds are equitably distributed among the creditors.
There are multiple definitions - click on the translation that matches your context.
the document filed with a court to start a bankruptcy proceeding
HM Revenue and Customs has applied for a bankruptcy petition saying Ms Radin failed to file tax returns for two years.