Inclusion Criteria:
* Histopathological diagnosis of amyloidosis based on detection by immunohistochemistry (IHC) and polarizing light microscopy of green birefringent material in Congo red-stained tissue specimens in an organ other than bone marrow, characteristic electron microscopy appearance, or mass spectrometry. Specifically for male subjects 70 years of age or older who have cardiac involvement only and subjects of African descent, mass spectrometry typing of AL amyloid in a tissue biopsy is recommended to rule out other types of amyloidosis such as age-related amyloidosis or hereditary amyloidosis (ATTR mutation)
* Must have evidence of high risk AL amyloidosis defined as one of the following any time within the 6 months prior to consent:
* Biomarker-based indicators of severe disease: NT-proBNP \> 8500 ng/L OR hs-cTnT \>= 50 ng/L
* BUMC 2019 stage 3b requiring both TnI \> 0.1 ng/mL and BNP \> 700 pg/mL
* Mayo 2012 stage 4 that includes each of the following a) cTnT \>= 0.025 ng/mL or hs-cTnT \>= 40 ng/mL; b) NT-proBNP \>= 1800 pg/mL; and c) dFLC \>= 180 mg/L
* Significant AL amyloid related hypotension (systolic blood pressure \[SBP\] \< 100 mm Hg or symptomatic orthostatic hypotension defined as a decrease in systolic blood pressure upon standing of \> 20 mm Hg despite medical management \[fludrocortisone, midodrine, etc\] in the absence of volume depletion)
* Absolute neutrophil count (ANC) \>= 1000/uL
* Platelet count \>= 50,000 and platelet transfusion independent for 1 week prior to screening
* Estimated creatinine clearance \>= 20 mL/min/1.73 m\^2 as defined by Chronic Kidney Disease Epidemiology Collaboration equation (CKD-EPI)
* Total bilirubin \< 1.5 x institutional upper limit of normal (IULN) except for patients with Gilbert syndrome in which case total bilirubin =\< 2 x IULN
* Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) \< 3 x IULN
* Left ventricular ejection fraction \>= 30%
* Females of childbearing potential (FCBP) must have a negative serum or urine pregnancy test with a sensitivity of at least 25 mIU/mL within 10 - 14 days prior to and again within 24 hours of starting study medication. The effects of protocol therapy on the developing human fetus are unknown. For this reason, FCBP and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry, for the duration of study participation, and for 5 months after completion of protocol therapy. Men must refrain from donating sperm during the same period that they must agree to use contraception. 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. A female of childbearing potential (FCBP) is a sexually mature woman who: 1) has not undergone a hysterectomy or bilateral oophorectomy; or 2) has not been naturally postmenopausal for at least 24 consecutive months (i.e., has had menses at any time in the preceding 24 consecutive months
* Ability to understand and the willingness to sign a written informed consent document
* Patients with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial
Exclusion Criteria:
* \> 1 prior line of therapy
* Refractory to any proteasome inhibitor
* Prior CD38 antibody exposure
* Cardiac exclusions:
* Subjects with a history of sustained ventricular tachycardia EXCEPT in patients with a pacemaker/implantable cardioverter defibrillator (ICD)
* Baseline QT interval as corrected by institutional rate correction algorithm (e.g. corrected QT interval by Bazett formula \[QTc\]B or corrected QT interval by Fridericia formula \[QTcF\]) \> 500 msec EXCEPT in patients with a pacemaker
* Grade 2 or greater peripheral sensory neuropathy
* Received any investigational drug within 14 days or 5 half-lives of the investigational drug, whichever is longer
* Hypersensitivity or history of intolerance to steroids, mannitol, pregelatinized starch, sodium stearyl fumarate, histidine (as base and hydrochloride salt), arginine hydrochloride, poloxamer 188, sucrose or any of the other components of study therapy that are not amenable to premedication with steroids and H2 blockers or would prohibit further treatment with these agents
* Human immunodeficiency virus (HIV) positive EXCEPT if the patient meets all the following: CD4 \> 350 cells/mm3, undetectable viral load, maintained on modern therapeutic regimen utilizing non CYP interacting agents (e.g. excluding ritonavir), and no untreated acquired immune deficiency syndrome defining opportunistic infections
* Seropositive for hepatitis B surface antigen \[HBsAg\]) EXCEPT subjects with resolved infection (i.e., subjects who are positive for antibodies to hepatitis B core antigen \[antiHBc\] and/or antibodies to hepatitis B surface antigen \[antiHBs\]) must be screened using real-time polymerase chain reaction (PCR) measurement of hepatitis B virus (HBV) deoxyribonucleic acid (DNA) levels. Those who are PCR positive will be excluded. Subjects with serologic findings suggestive of HBV vaccination (antiHBs positivity as the only serologic marker) AND a known history of prior HBV vaccination, do not need to be tested for HBV DNA by PCR
* Seropositive for hepatitis C EXCEPT in the setting of a sustained virologic response \[SVR\], defined as without viremia for at least 12 weeks after completion of antiviral therapy
* Polyneuropathy, organomegaly, endocrinopathy, monoclonal protein, and skin changes (POEMS) syndrome, wild type or mutated (ATTR) amyloidosis, and Waldenstrom macroglobulinemia
* Known allergies, hypersensitivity, or intolerance to monoclonal antibodies, hyaluronidase, human proteins, or their excipients (refer to investigational brochure \[IB\]), or known sensitivity to mammalian-derived products
* Patients who have had any plasma cell directed treatment, radiotherapy, plasmapheresis, or major surgery (as defined by the investigator) within 1 week prior to cycle 1 day 1 of the study. Patients may be receiving concomitant therapy with low dose corticosteroids (e.g., prednisone up to but no more than 10 mg by mouth daily or its equivalent) for symptom management and comorbid conditions
* Concurrent medical condition or disease (e.g., active infection requiring treatment with a parenteral antibiotic, active tuberculosis, etc) that would expose excessive risk to the patient or may interfere with compliance or interpretation of the study results
* Known or suspected of not being able to comply with the study protocol (e.g. alcoholism, drug dependency, or psychological disorder) or the subject has any condition for which, in the opinion of the investigator, participation would not be in the best interest of the subject (e.g., compromise their well-being) or that could prevent, limit, or confound the protocol-specified assessments
* Pregnant women are excluded from this study because protocol therapy has the potential for teratogenic or abortifacient effects. Because there is an unknown but potential risk for adverse events in nursing infants secondary to protocol treatment of the mother, breastfeeding should be discontinued. Women planning to become pregnant 1 year after discontinuation of cyclophosphamide or 3 months following discontinuation of isatuximab
