This trial is for patients with bronchiectasis who completed the Boehringer Ingelheim 1397-0012 Airleaf parent study. This is a continuation of the Airleaf study and is meant to assess the long-term safety, effectiveness, and tolerability of the study drug (BI 1291583). Approximately 220 patients will be enrolled into the study and will be randomized into either 1 milligram, 2.5 milligram, or 5 milligram study drug or placebo. Patients will be treated for approximately 1 year, while study staff monitor the number of patient pulmonary exacerbations.