The Archdiocese of Portland was the first to do it. Three months later the Roman Catholic Diocese in Tucson, Ariz., followed suit and three months after that the diocese in Spokane, Wash., did it, too.

They all filed for bankruptcy and since then more than 15 other Catholic dioceses and religious orders have filed for bankruptcy to seek protection from lawsuits by sexual-assault victims, resulting in about 4,000 claims seeking compensation for past wrongdoing. This year, three more Catholic dioceses announced intentions to...