Olaparib in Patients With HRD Malignant Mesothelioma

Inclusion Criteria: * Must have a medical diagnosis of malignant mesothelioma that has been confirmed by a physician. * Participant must be able to sign a consent form stating that they choose (of their own free will) to participate in the study and agree to follow the study requirements and restrictions that are listed in the consent form. * Must be willing to sign and date consent form before any mandatory study-specific procedures, sample collecting and tests. * Willing to experience genetic testing to determine study eligibility. Must be willing to genetically test tumor and normal body cells. * Before participating in the treatment phase of this study, participants must be willing to give their own consent (agreement) to have their samples collected for genetic and biomarker research. * Age 18 or older. * Participant must show evidence of specific DNA changes/genetic mutations defined as follows: A) BAP1 loss (the loss of a protein called ubiquitin carboxyl-terminal hydrolase) verified by physicians at the University of Chicago using sampling tests AND/OR B) A mutation (abnormal change) in the participant's germ cells (reproductive cells) or somatic cells (non-reproductive cells) that disrupts protein function in at least one of the patient's genes. * Prior treatment with cisplatin or carboplatin is required. * Patients must have platinum-sensitive disease (cancer that responds to treatments with anticancer drugs containing metal platinum). For eligibility in this study, platinum-sensitive disease will be defined as no disease progression while on a platinum agent (chemotherapy drug) or for at least 3 months after completing treatment with a platinum agent. * Patients must have normal organ and bone marrow function measured within 28 days prior to receiving study treatment. Normal bone marrow and organ function will be assessed using specific lab tests/ criteria set by the study's lead physician. * Eastern Cooperative Oncology Group (ECOG) performance status 0-1. * Patients must have a life expectancy of 16 weeks or more. * Must have a tumor that can be measured according to criteria set by the modified Response Evaluation Criteria in Solid Tumors (RECIST) standards for pleural mesothelioma and RECIST 1.1 for peritoneal and tunica vaginalis mesothelioma. Patients in the study must have at least one area of damaged tissue (a lesion) that has not received previous radiation treatment. This damaged tissue must be accurately measured at the beginning of the study as greater than or equal to 10 mm in the longest diameter (except lymph nodes which must have short axis greater than or equal to 15 mm). The patient's tumor would be measured using computed tomography (CT), which is suitable for accurate repeated measurements. * Both male and female patients can participate in this study. * If a woman is of childbearing potential and wishes to participate in the study, she most show evidence that she is not pregnant using a negative urine or serum pregnancy test within 28 days of study treatment and confirmed prior to treatment on day 1. * Women who are postmenopausal and wish to participate in the study, must also show evidence of postmenopausal status. Postmenopausal status will be defined as: 1) A woman who does not experience menstruation (known as amenorrhea) for 1 year or more following the end of hormonal treatments. 2) Women who have reproductive/hormone levels in the post-menopausal range for women under 50 as confirmed by medical tests; 3) Radiation-induced oophorectomy (removal of one or more ovaries) with last menses greater than 1 year ago; 4) Menopause caused by chemotherapy with greater than 1 year since last menses 5) Surgical sterilization (bilateral oophorectomy or hysterectomy). * Male patients must use a condom during treatment and for 3 months after the last dose of study drug (olaparib) when having sexual intercourse with a pregnant woman or with a woman of childbearing potential. Female partners of male patients should also use a highly effective form of contraception if they are of childbearing potential. * NOTE 1: Tests to confirm the eligibility of participants who have the above mutations (altered germ or somatic cells) will take place at a germline or tumor sequencing lab that is certified under the Clinical Laboratory Improvement Amendments (CLIA). Eligibility of study participants will be confirmed once the physical leading this study receives the official mutation report from the lab and confirms that the participant's identified mutation fits the definition outlined above. All other patients must consent to tumor and normal sample sequencing as described in study procedures below during the prescreening phase to determine eligibility. * NOTE 2: Rare exceptions of participants who may have conflicting evidence regarding protein function will be interpreted on an individual basis by the physician leading the study. Exclusion criteria: Medical conditions: * Any evidence of uncontrollable illness that the physician leading this study deems undesirable for the patient to participate in the trial. * Other malignancy (tumor/cancer) unless it has been treated with no evidence of disease for 3 or more years except: adequately treated non-melanoma skin cancer, curatively treated in situ cancer of the cervix, ductal carcinoma in situ (DCIS), Stage 1, grade 1 endometrial carcinoma. * Patients with BAP1 tumor predisposition syndrome will be included in the trial. These patients may be eligible if they have a history of syndrome-related cancers, provided they completed their surgery and chemotherapy more than three years prior to registration, and the patient remains free of disease that continues to re-occur or spread to other parts of the body. * Patients with cancer that does not respond to platinum chemotherapy drugs (known as platinum-resistant disease), defined as disease progression during or within 3 months of receiving chemotherapy. * Resting electrocardiogram (E