Actually, there is likely room for bankruptcy law and statutes of limitations in halacha.
Statutes of limitations are discussed expressly in at least one Teshuv cited by the Pischei Teshuva in the early simanim of Choshen Mishpat (I can’t find the exact place right now, I will continue looking). Statute of limitations may be imposed as a communal enactment for the same reasons statutes of limitations exist in secular law systems – to provide defendants with security, to encourage plaintiff’s to bring their claims early while evidence is fresh, ect. The statute of limitations only binds those in the community in which it is enacted. Thus, if Reuvain from New York (which enacted a statute of limitations) brings a suit against Shimon in Lakewood (which has not statute of limitations), Shimon may not be able to claim the benefit of the New York statute of limitations (though this might depend on which city’s Beis Din the case is brought in).
As for bankruptcy law, it is true, there is always a chiyuv to repay money that is owed. However, Halachah does allow local communities to prioritize which creditors of an insolvent debtor will be paid in what order. For example, a community may decide that a bankrupt’s unpaid school tuition and shul membership dues must be paid first, while loans taken from individuals are paid second, loans from banks or businesses third, and unpaid tzedaka pledges last. Hakol l’fi minhag hamakom.