: 1. Participants with histologically confirmed unresectable advanced or metastatic solid tumours who have documented progression after or are refractory to or ineligible for established and available therapies with proven clinical benefit, or have declined such therapy. 2. At least one measurable disease lesion outside of the central nervous system (CNS) defined per Response Evaluation Criteria in Solid Tumours (RECIST) v1.1 3. Patients with brain metastases are eligible provided they meet the following criteria: - Brain metastases have adequately been treated and are without progression or haemorrhage and are considered stable and asymptomatic by the investigator, - Radiotherapy and/or surgery for brain metastases was completed at least 14 and 28 days, respectively, prior to the first administration of BI 3819026, - Patient is off steroids and anti-convulsive drugs for at least 7 days prior to the first administration of BI 3819026 and has no requirement for such therapy at the time of initiating trial treatment. 4. Availability of archived formalin-fixed and paraffin embedded (FFPE) tumour tissue. Patients who do not have archived FFPE tumour tissue available may be allowed to enrol without archival tumour tissue upon agreement between the investigator and the Sponsor 5. All toxicities related to previous anti-cancer therapies have resolved to Grade ≤1 or baseline prior to trial treatment administration (except for alopecia, peripheral neuropathy and endocrinopathies considered irreversible [like hypothyroidism], and amenorrhea/menstrual disorders which can be any grade) 6. Adequate liver, bone marrow and renal organ function Further inclusion criteria apply.

: 1. Previous or concomitant malignancies other than the one treated in this trial within the last 3 years except: - Effectively treated non-melanoma skin cancers - Effectively treated carcinoma in situ of the cervix - Effectively treated ductal carcinoma in situ of the breast - Other effectively treated malignancy that is considered cured by local treatment 2. Has received prior therapy with an immune-checkpoint inhibitor that was discontinued due to immune-related adverse events (AE) 3. Prior treatment with systemic anti-cancer drugs (including any agents or investigational medicinal products) within 3 weeks or 5 half-lives (whichever is shorter) before the first dose of trial treatment 4. Radiotherapy within 4 weeks prior to start of the trial treatment except as follows: - Palliative radiotherapy to regions other than the chest is allowed if completed at least 2 weeks prior and is not on the target lesion (which should be outside of the radiation field) - Single dose palliative radiotherapy for symptomatic metastasis that is not the target lesion (which should be outside of the radiation field) within 2 weeks prior may be allowed 5. Active/previous history of interstitial lung disease, pulmonary fibrosis, organising pneumonia or non-infectious pneumonitis (any grade) 6. Patients with active autoimmune disease or a documented history of autoimmune disease, that requires systemic treatment, e.g. corticosteroids or immunosuppressive drugs, except patients with vitiligo, resolved childhood asthma/atopy, alopecia, or any chronic skin condition that does not require systemic therapy; patients with autoimmune-related hypothyroidism on a stable dose of thyroid replacement hormone and/or controlled Type 1 diabetes mellitus on a stable insulin regimen are eligible 7. Patient has a diagnosis of immunodeficiency other than human immunodeficiency virus (HIV) 8. Patients with history of HIV infection who meet one or more of the following criteria: - CD4+ count <350 cells/µL - Viral load >400 copies/mL - Not receiving antiretroviral therapy - Receiving established antiretroviral therapy for less than four weeks prior to the start of trial treatment - History of acquired immunodeficiency syndrome (AIDS)-defining opportunistic infections within 12 months prior to start of trial treatment Patients with a history of HIV who do not meet any of the exclusion criteria above are eligible to participate but the patient must be under the care of an HIV/Infectious Diseases specialist, or an HIV/Infectious Diseases specialist must be consulted prior to inclusion Further exclusion criteria apply.