Ibrutinib With or Without Bortezomib and Dexamethasone in Treating Patients With Relapsed or Refractory Immunoglobulin Light Chain Amyloidosis

Criteria: * Measurable disease of AL amyloidosis as defined by at least ONE of the following: * Serum monoclonal protein \>= 1.0 by protein electrophoresis * \> 200 mg of monoclonal protein in the urine on 24 hour electrophoresis * Free light chains (abnormal absolute value, ratio and the dFLC \> 5 mg/dL) Inclusion Criteria: * Histological diagnosis of AL amyloidosis as based on detection by polarizing microscopy of green birefringent material in Congo red-stained tissue specimens; the type must have been confirmed unequivocally * Must have had one prior line of systemic therapy for AL; Note: patients who do not achieve at least a PR to frontline therapy in 3 months may be eligible after discussion with study chair * Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0, 1 or 2 * Absolute neutrophil count (ANC) \>= 1000/mm\^3 * Platelet count \>= 100,000/mm\^3 or \>= 50,000/mm\^3 if bone marrow involvement independent of transfusion support in either situation * Hemoglobin \>= 8.0 g/dL * Total bilirubin =\< 1.5 x upper limit of normal (ULN) unless due to Gilbert's syndrome or of non-hepatic origin * Aspartate transaminase (AST) =\< 3 x upper limit of normal (ULN) * Alanine aminotransferase (ALT) =\< 3 x ULN * Creatinine =\< 3 mg/dL and creatinine clearance (CrCL) \>= 25 ml/min * Negative serum pregnancy test done =\< 7 days prior to registration, for persons of childbearing potential only * Ability to complete questionnaire(s) by themselves or with ass…