A Study to Test How Well BI 1291583 is Tolerated by People With Cystic Fibrosis Bronchiectasis (Clairafly™)

Inclusion Criteria: 1. Age of patients when signing the informed consent ≥18 years 2. Historical clinical diagnosis of Cystic fibrosis (CF) (symptoms of CF and sweat chloride ≥ 60 mmol/L and/or 2 CF-causing Cystic fibrosis transmembrane conductance regulator (CFTR) mutations) 3. Investigator-confirmed diagnosis of Bronchiectasis (BE) by Computed tomography (CT) scan and clinical history consistent with BE (e.g., cough, chronic sputum production, recurrent respiratory infections). Subjects whose past chest CT records are not available will undergo a chest CT scan during Screening. Historical scans must not be older than 5 years 4. History of pulmonary exacerbations requiring antibiotic treatment. In the 12 months before Visit 1, patients must have had either: 1. at least 2 exacerbations, or 2. at least 1 exacerbation and an St. George's Respiratory Questionnaire (SGRQ) Symptoms score of \>40 at screening visit 1 For patients on stable oral or inhaled antibiotics as chronic treatment for BE, at least one exacerbation must have occurred while on stable antibiotics. 5. Patients must be able to provide spontaneous or induced sputum samples. Further inclusion criteria apply. Exclusion Criteria: 1. Moderate or severe liver disease (defined by Child-Pugh score B or C hepatic impairment) or Aspartate aminotransferase (AST) and/or Alanine aminotransferase (ALT) \> 3.0x Upper limit of normal (ULN) at Visit 1 2. Estimated glomerular filtration rate (eGFR) according to Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) formula \< 30 mL/min at Visit 1 3. Absolute blood neutrophil count \< 1,000/mm\^3 (equivalent to \< 1000 cells/μL or \< 10\^9 cells/L) at Visit 1 4. Any findings in the medical examination (including blood pressure (BP), pulse rate (PR), or electrocardiogram (ECG)) and/or laboratory value assessed at Visit 1 or during screening period that in the opinion of the investigator may put the patient at risk by participating in the trial 5. Positive serological tests for hepatitis B, hepatitis C (also confirmed with Hepatitis C virus ribonucleic acid (HCV RNA)), or human immunodeficiency virus (HIV) infection, or known infection status. Further exclusion criteria apply.