Fulvestrant With or Without Bortezomib in Patients With Inoperable Locally Advanced or Metastatic Estrogen Receptor Positive Breast Cancer

Inclusion Criteria: * ELIGIBILITY CRITERIA FOR ARM A AND ARM B * Patients must have histologically or cytologically confirmed ER+ positive breast cancer * Patients must be postmenopausal, defined as: (1) a history of at least 12 months without spontaneous menstrual bleeding, (2) prior bilateral salpingo-oophorectomy, with or without hysterectomy, (3) age \>= 55 years with a prior hysterectomy with or without oophorectomy, (4) age \< 55 years with a prior hysterectomy without oophorectomy or unknown status, with a documented follicle-stimulating hormone (FSH) level in postmenopausal range within 4 week s of registration, (5) receiving a gonadotropin releasing hormone analog (GnRH) to suppress ovarian function (eg, goserelin 3.6 mg every \[q\] 4 weeks) * Patients must have stage IV disease or inoperable locally advanced disease * Patients may have measurable disease only, non-measurable disease only, or both (Response Evaluation Criteria in Solid Tumors \[RECIST 1.1\]); it is anticipated that at least 50% of patients will have only non-measurable disease * Patients are required to have disease that is resistant to aromatase inhibitor (AI), which is defined either as relapse while receiving adjuvant A.I. therapy (ie, anastrazole, letrozole, or exemestane), and/or disease progression after one or more A.I.s for metastatic disease; prior exposure to more than one AI is permitted * Patient may have had prior tamoxifen but are not required to * Patients may have received up to one prior chemotherapy regimen for metastatic disease * Patients may have received prior bevacizumab * Patients who have received up to 2 doses of fulvestrant given within a 4 week period prior to registration are eligible; the interval between the first fulvestrant dose and registration must be 6 weeks or less; patients may have received EITHER 250 mg or 500 mg of fulvestrant previously; if the patient has received 250 mg, they will receive the 500 mg loading dose on study day -14; if they already received 500 mg, they will begin the study on day +1 * Life expectancy of greater than 3 months * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 60%) * Leukocytes \>= 3,000/mcL * Absolute neutrophil count \>= 1,500/mcL * 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 \[SGPT\]) =\< 2.5 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 * Patients must be disease-free of prior invasive malignancies for \>= 5 years with the exception of: curatively-treated basal cell or squamous cell carcinoma of the skin, carcinoma in situ of the cervix * Patients must have the ability to understand and the willingness to sign a written informed consent document * 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 participating in this study, she should inform her treating physician immediately * ELIGIBILITY CRITERIA FOR ARM C * Previously met all eligibility criteria for arms A and B and registered on trial to arm A (fulvestrant alone) * Disease progression on arm A and agreeable to crossover to arm C * Has received no intervening therapy (ie, alternative endocrine therapy, chemotherapy, biologic therapy) between disease progression on arm A and registration an arm C * ECOG performance status 0-2 * Tumor measurements (eg, computed tomography \[CT\] scan of chest/abdomen/pelvis) within 4 weeks of registration to arm C * Leukocytes \>= 3,000/mcL, within 2 weeks of registration on arm C * Absolute neutrophil count \>= 1,500/mcL, within 2 weeks of registration on arm C * Platelets \>= 100,000/mcL, within 2 weeks of registration on arm C * Total bilirubin within normal institutional limits, within 2 weeks of registration on arm C * AST(SGOT)/ALT(SGPT) =\< 2.5 x institutional upper limit of normal, within 2 weeks of registration on arm C * Creatinine within normal institutional limits, within 2 weeks of registration on arm C OR creatinine clearance \>= 60 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal, within 2 weeks of registration on arm C Exclusion Criteria: * EXCLUSION CRITERIA FOR ARM A AND ARM B * Patients who have had chemotherapy or radiotherapy within 4 weeks (6 weeks for nitrosoureas or mitomycin C) prior to entering the study or those who have not recovered from adverse events due to agents administered more than 4 weeks earlier * Patients may not be receiving any other investigational agents * Patients with known brain metastases should be excluded from this clinical trial * Presence of rapidly progressive, life-threatening metastases; this includes patients with extensive hepatic involvement (\> 50% of the liver involved), symptomatic lymphangitic metastases, or brain or leptomeningeal involvement * History of allergic reactions attributed to compounds of similar chemical or biologic composition to bortezomib or fulvestrant * Patients who are concomitantly receiving bortezomib and drugs that are inhibitors or inducers of cytochrome P450 3A4 should be closely monitored for either toxicities or reduced efficacy * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements * Human immunodeficiency virus (HIV)-positive patients on combination antiretroviral therapy are ineligible * Patients who have previously received fulvestrant * Patients who have previously received bortezomib * Concomitant anticancer treatment with the following exceptions: (1) bisphosphonates for bone metastases, (2) a GnRH analog is permitted if the patient had progressive disease on a GnRH analog plus a selective estrogen receptor modulators (SERMs) or an AI; the GnRH analog may continue but the SERM or AI must be discontinued * Grade 2 or more peripheral neuropathy