Bortezomib, Cyclophosphamide, and Dexamethasone in Treating Patients With Primary Systemic Light Chain Amyloidosis

Inclusion Criteria: * Histochemical diagnosis of amyloidosis as based on detection by polarizing microscopy of green birefringent material in Congo red-stained tissue specimens * Measurable disease of amyloid light chain amyloidosis as defined by at least ONE of the following: serum monoclonal protein \>= 1.0 g by protein electrophoresis, \> 200 mg of monoclonal protein in the urine on 24 hour electrophoresis, serum free light-chain \>= 7.5 mg/dL with an abnormal kappa:lambda ratio * Eastern Cooperative Oncology Group (ECOG) Performance Status (PS) 0, 1 or 2 * Absolute neutrophil count \>= 1000/uL * Platelet \>= 75000/uL * Total bilirubin \< 3.0 mg/dL * Aspartate aminotransferase (AST) =\< 3 x upper limit of normal (ULN) * Creatinine clearance \>= 30ml/min * Women of childbearing potential should have a negative serum or urine pregnancy test done =\< 7 days prior to registration, and should be willing to use an acceptable method of birth control (i.e., a hormonal contraceptive, intra-uterine device, diaphragm with spermicide, condom with spermicide, or abstinence) for the duration of the study * Male subject agrees to use an acceptable method for contraception for the duration of the study * Previously treated amyloidosis; no limit to prior therapy provided there is adequate residual organ function * Symptomatic organ involvement (heart, kidney, liver/GI tract, peripheral nervous system or soft tissue); carpal tunnel syndrome skin purpura, or the presence of vascular amyloid on a bone marrow biopsy alone are not sufficient to meet criteria for "symptomatic organ involvement" * Renal involvement is defined as proteinuria (predominantly albumin) \> 0.5 g/day in a 24- hour urine collection * Cardiac involvement is defined as the presence of a mean left ventricular wall thickness on echocardiogram greater than 12 mm in the absence of a history of hypertension or valvular heart disease, or in the presence of unexplained low voltage (\< 0.5 mV) on the electrocardiogram * Hepatic involvement is defined as hepatomegaly (\>= 2 cm below costal margin) on physical exam or an alkaline phosphatase \> 1.5 x ULN * Peripheral nerve involvement is defined based on clinical history or abnormal sensory and/or motor findings on neurologic exam * Autonomic nerve involvement is defined as orthostasis, symptoms of nausea or dysgeusia, gastric atony by gastric emptying scan, diarrhea or constipation * Soft tissue and lymphatic involvement may be ascertained based on classic physical exam findings (macroglossia, shoulder pad sign, raccoon eyes, carpal tunnel syndrome, synovial enlargement, firm enlarged lymph nodes) or biopsy * Voluntary written informed consent before performance of any study-related procedure not part of normal medical care, with the understanding that consent may be withdrawn by subject any time without prejudice to future medical care * Willingness to return to Mayo Clinic enrolling institution for follow-up Exclusion Criteria: * Melphalan or other myelosuppressive agents =\< 3 weeks prior to registration; non-myelosuppressive agents like thalidomide, or high dose corticosteroids \<= 1week prior to registration * Concurrent use of corticosteroids, but patients may be on chronic steroids (maximum dose 20 mg/day prednisone equivalent) if they are being given for disorders other than amyloid, i.e., adrenal insufficiency, rheumatoid arthritis, etc * Any of the following because this study involves an agent whose genotoxic, mutagenic and teratogenic effects on the developing fetus and newborn are unknown: pregnant women and nursing women * Other active malignancy =\< 2 years prior to registration; EXCEPTIONS: Nonmelanotic skin cancer or carcinoma-in-situ of the cervix; NOTE: If there is a history or prior malignancy, they must not be receiving any specific treatment for their cancer * Co-morbid systemic illnesses or other severe concurrent disease which, in the judgment of the investigator, would make the patient inappropriate for entry into this study or interfere significantly with the proper assessment of safety and toxicity of the prescribed regimens including psychiatric illness/social situations that would limit compliance with study requirements * Known to be HIV positive * Receiving any other investigational agent which would be considered as a treatment for the primary neoplasm * Clinically overt multiple myeloma (monoclonal Bone Marrow Plasma Count \> 30%), and at least one of the following: bone lesions or hypercalcemia * History of myocardial infarction =\< 6 months, or requiring use of ongoing maintenance drug therapy for life-threatening ventricular arrhythmias * Grade 3 sensory or grade 1 painful peripheral neuropathy * Known hypersensitivity to bortezomib, boron or mannitol * Cardiac syncope, uncompensated New York Heart Association (NYHA) Class 3 or 4 congestive heart failure or troponin T \> 0.1 ng/mL