PI3Kbeta Inhibitor AZD8186 and Docetaxel in Treating Patients Advanced Solid Tumors With PTEN or PIK3CB Mutations That Are Metastatic or Cannot Be Removed by Surgery

Inclusion Criteria: * Patients must have histologically confirmed malignancy that is metastatic or unresectable and for which standard curative or palliative measures do not exist or are no longer effective * Patients must be able to swallow and retain oral medications and be without gastrointestinal illnesses that would preclude absorption of AZD8186 * Unlimited prior therapies allowed * Docetaxel appropriate * Patients who have not received prior docetaxel (or other taxane therapy) in the advanced setting are eligible for all cohorts * Patients who have previously received docetaxel (or other taxane therapy) in the advanced setting are eligible for the dose escalation cohort only, if anticipated to have maintained taxane sensitivity and in the opinion of the investigator would still benefit from further docetaxel therapy * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 60%) * Leukocytes \>= 3,000/mcL * Absolute neutrophil count \>= 1,500/mcL * Hemoglobin \>= 8 g/L * Platelets \>= 100,000/mcL * Total bilirubin within normal institutional limits * Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 1.5 x institutional upper limit of normal * Creatinine within normal institutional limits OR creatinine clearance \>= 60 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal * PTEN or PIK3CB mutated advanced solid tumor * PTEN loss of function mutation or PIK3CB gain of function mutation identified by local Clinical Laboratory Improvement Act (CLIA) certified next generation sequencing (NGS) * Breast cancers patients enrolled on this study must have either: * Estrogen receptor positive and HER2 negative breast cancer * Triple negative breast cancer * Adequate archival tissue (metastatic tissue sample is preferable but primary tumor tissue will be acceptable) or willing to undergo pre-treatment biopsy (for central confirmation of molecular alteration and PTEN immunohistochemical assessment) if adequate archival tissue is unavailable * The effects of AZD8186 on the developing human fetus are unknown; for this reason, women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation; should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately; men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of study participation, and 4 months after completion of AZD8186 administration * Ability to understand and the willingness to sign a written informed consent document * DOSE ESCALATION COHORT: Prior receipt of docetaxel is permitted * DOSE ESCALATION COHORT: Measurable disease is not required for enrollment * PHARMACODYNAMIC EXPANSION COHORT: Prior receipt of docetaxel is not permitted * PHARMACODYNAMIC EXPANSION COHORT: Patients must have measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded for non-nodal lesions and short axis for nodal lesions) as \>= 20 mm (\>= 2 cm) by chest x-ray or as \>= 10 mm (\>= 1 cm) with computed tomography (CT) scan, magnetic resonance imaging (MRI), or calipers by clinical exam * PHARMACODYNAMIC EXPANSION COHORT: Consent to allow mandatory paired (pre- and on- treatment) fresh tissue biopsies if deemed safe to do so for quantitation of Akt pathway signaling proteins * DISEASE SPECIFIC EXPANSION COHORTS: Prior receipt of docetaxel is not permitted * DISEASE SPECIFIC EXPANSION COHORTS: Patients (excepting the prostate cancer patients) must have measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded for non-nodal lesions and short axis for nodal lesions) as \>= 20 mm (\>= 2 cm) by chest x-ray or as \>= 10 mm (\>= 1 cm) with CT scan, MRI, or calipers by clinical exam * DISEASE SPECIFIC EXPANSION COHORTS: Breast cancers patients enrolled on this study must have: * Metastatic or advanced (incurable and unresectable) HER2 negative breast cancer regardless of estrogen receptor status (both hormone receptor positive and triple negative patients are eligible) * Received hormonal therapy, as appropriate based on their hormone receptor status; hormone receptor positive patients who have not received endocrine therapy for recurrent/metastatic disease are eligible, permitted their physician feels they are not appropriate for first line endocrine therapy, for example for high risk visceral metastatic disease * DISEASE SPECIFIC EXPANSION COHORTS: Prostate cancers patients enrolled on this study (applies to all prostate cancer patients treated on parts 1, 2, and 3) must have: * Metastatic or advanced (incurable and unresectable) castration resistant metastatic cancer * Received at least one additional line of anti-androgen therapy with abiraterone or enzalutamide * Measurable disease is not required for enrollment Exclusion Criteria: * HER2 positive breast cancer * Prior treatment with PI3K/AKT inhibitors * Any known concurrent RAF or PIK3CA mutation * Patients who have had chemotherapy, radiotherapy, immunotherapy or anticancer agents within 4 weeks (6 weeks for nitrosoureas or mitomycin C) of the first dose of study treatment, except hormonal therapy with luteinizing hormone-releasing hormone (LHRH) analogues for medical castration in patients with prostate cancer and breast cancer, which are permitted * Patients who have not recovered from adverse events due to prior anti-cancer therapy (i.e., have residual toxicities \> grade 1) * Patients who are receiving any other investigational agents * Patients with known, untreated or unstable brain metastases should be excluded from this clinical trial because of their poor prognosis and because they often develop progressive neurologic dysfunction that would confound the evaluation of neurologic and other adverse events; patients with treated brain metastases are eligible if the metastases have been radiographically and clinically stable for at least one month; if on steroids for this indication, the patient must be on a stable dose for at least one month * History of clinically significant allergic reactions attributed to compounds of similar chemical or biologic composition to AZD8186 or docetaxel or to docetaxel itself * Patients receiving any medications or substances that are strong inhibitors and/or strong or moderate inducers of CYP3A4 are ineligible; because the lists of these agents are constantly changing, it is important to regularly consult a frequently-updated medical reference; as part of the enrollment/informed consent procedures, the patient will be counseled on the risk of interactions with other agents, and what to do if new medications need to be prescribed or if the patient is considering a new over-the-counter medicine or herbal product * Existing bleeding or condition associated with increased risk of bleeding * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, uncontrolled hypertension, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements * Pregnant women are excluded from this study because AZD8186 is a PI3K inhibitor with the potential for teratogenic or abortifacient effects; because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with AZD8186, breastfeeding should be discontinued if the mother is treated with AZD8186; these potential risks may also apply to other agents used in this study * Human immunodeficiency virus (HIV)-patients positive for human immunodeficiency virus (HIV) are NOT excluded from this study, but HIV-positive patients must have: * A stable regimen of highly active anti-retroviral therapy (HAART) that does not include strong inhibitors and strong or moderate inducers of CYP3A4 * No requirement for concurrent antibiotics or antifungal agents for the prevention of opportunistic infections * A CD4 count above 250 cells/mcL and an undetectable HIV viral load on standard polymerase chain reaction (PCR)-based test