A Study of Galunisertib on the Immune System in Participants With Cancer

Inclusion Criteria: * Have a confirmed diagnosis of advanced, refractory solid tumors and tumor progression or treatment intolerance to at least 1 prior therapy. * Have measurable disease that is amenable to a radiographic or ultrasound-guided biopsy or may be biopsied in the office without radiologic guidance. * Have a performance status of ≤2 on the Eastern Cooperative Oncology Group (ECOG) scale. * Have discontinued all disease-modifying therapy for the primary cancer for 28 days prior to initiation of study treatment. * Hepatic: bilirubin ≤1.5 times upper limits of normal (ULN), alanine aminotransferase (ALT) and aspartate transaminase (AST) ≤3.0 times ULN. For participants with tumor involvement of the liver, AST and ALT equaling ≤5.0 times ULN are acceptable. Alkaline phosphatase ≤5.0 times ULN for participants with tumor involvement of the bone is acceptable. * Have adequate renal function, defined as serum creatinine levels ≤2.0 ULN or calculated creatinine clearance \>45 mL/min. * Male and female participants with reproductive potential must use an approved contraceptive method, if appropriate (for example, intrauterine device, birth control pills, or barrier device) during and for 6 months after discontinuation of study treatment. * Women of childbearing potential must have a negative beta-human chorionic gonadotropin pregnancy test documented within 7 days prior to treatment. Have given written informed consent prior to any study-specific procedures. * Are willing and able to comply with study procedures and instructions, including completion of diaries. * Must have received at least 1 prior approved immunotherapy or chemotherapy; however, not within 28 days of the initial dose of study drug. May have received prior radiotherapy for their malignancy. * May have received treatment with an investigational product. Exclusion Criteria: * Are enrolled in any other type of medical research judged not to be scientifically or medically compatible with this study within 28 days of the initial dose of study drug. * Have moderate or severe cardiac disease: * Have the presence of cardiac disease, including a myocardial infarction within 6 months prior to study entry, unstable angina pectoris, New York Heart Association Class III/IV congestive heart failure, or uncontrolled hypertension. * Have documented major electrocardiogram (ECG) abnormalities (not responding to medical treatments) at the investigator's discretion (for example, symptomatic or sustained atrial or ventricular arrhythmias, second- or third-degree atrioventricular block, complete bundle branch block, ventricular hypertrophy, or recent myocardial infarction). * Have major abnormalities documented by echocardiography (ECHO) with Doppler (for example, moderate or severe heart valve function defect and/or left ventricular ejection fraction \<50%, evaluation based on the institutional lower limit of normal). * Have predisposing conditions that are consistent with development of aneurysms of the ascending aorta or aortic stress (for example, family history of aneurysms, Marfan-Syndrome, bicuspid aortic valve, evidence of damage to the large vessels of the heart documented by computed tomography (CT) scan with contrast). * Are women who are pregnant or lactating. * Have a serious concomitant systemic disorder (for example, active infection including human immunodeficiency virus \[HIV\], hepatitis C virus \[HCV\], hepatitis B virus \[HBV\] \[ie, positive hepatitis B surface antigen \[+HBsAg\]\]), or an autoimmune disease. * Have a second primary malignancy or any history in any time frame of a prior malignancy. * Are unwilling or unable to participate in, or do not have tissue adequate for participation in the biomarker analyses in the study.