Doxorubicin, Vinblastine, Dacarbazine, Brentuximab Vedotin, and Nivolumab in Treating Patients With Stage I-II Hodgkin Lymphoma

Inclusion Criteria:

* Measurable disease (\>= 1.5 cm) as assessed by 2 dimensional measurement by computed tomography (CT)
* Previously untreated stage I or II non-bulky (defined as a mass measuring \< 10 cm in the longest dimension by CT) classical Hodgkin lymphoma
* Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0-2
* Life expectancy \>= 3 months
* Documented negative serologic testing for human immunodeficiency virus (HIV), hepatitis B (unless serologically positive due to prior vaccination), and hepatitis C =\< 1 year prior to registration
* White blood cell \>= 2,000 /mm\^3 without transfusion support \> 7 days prior to registration
* Hemoglobin \>= 8.5 g/dL without transfusion support \> 7 days prior to registration
* Absolute neutrophil count (ANC) \>= 1,000 cells/mm\^3 without transfusion support \> 7 days prior to registration
* Platelet count \>= 75,000/mm\^3 without transfusion support \> 7 days prior to registration
* Alanine and aspartate aminotransferase (ALT/AST) =\< 2.5 x upper limit of normal (ULN) obtained =\< 14 days prior to registration
* Total serum bilirubin =\< 1.5 x ULN (if documented Gilberts syndrome =\< 3 x ULN) obtained =\< 14 days prior to registration
* Serum creatinine =\< 1.5 x ULN or measured calculated creatinine clearance \>= 40 ml/min for subject with creatinine levels \> 1.5 x institutional ULN (per Cockcroft-Gault formula) obtained =\< 14 days prior to registration
* Negative serum pregnancy test (minimum sensitivity 25 IU/L or equivalent units of human chorionic gonadotropin \[HCG\]) within 7 days prior to registration in women of child-bearing potential (WOCBP)
* Sexually active female of reproductive capability ie, WOCBP, has agreed to use a medically accepted form of contraception from time of registration to completion of study therapy through 24 weeks (6 months) after last dose of NVB or BV; Note: Females of non-child-bearing potential are those who are postmenopausal for \> 1 year or who have had a bilateral tubal ligation or hysterectomy
* Male subjects agree to use an adequate method of contraception starting with the first dose of study therapy through 31 weeks after the last dose of study therapy
* Provide informed written consent
* Willing to return to enrolling institution for follow-up (during the active monitoring phase of the study)

  * Note: During the active monitoring phase of a study (i.e., active treatment and observation), participants must be willing to return to the consenting institution for follow-up

Exclusion Criteria:

* Any of the following because this study involves an investigational agent whose genotoxic, mutagenic and teratogenic effects on the developing fetus and newborn are unknown:

  * Pregnant women
  * Nursing women
  * Men or women of childbearing potential who are unwilling to employ adequate contraception
* Prior therapies including involved field radiation therapy
* Bulky disease (defined as a nodal mass measuring \>= 10 cm by CT)
* Known central nervous system (CNS) involvement
* Moderate or severe hepatic insufficiency Child-Pugh score \> 6
* Severe renal impairment (i.e. creatinine clearance \< 40 mL/min)
* Symptomatic cardiac disease including ventricular dysfunction, left ventricular ejection fraction \< 45%, symptomatic coronary artery disease or symptomatic arrhythmias
* Diagnosis of immunodeficiency or is receiving systemic steroid therapy or any other form of immunosuppressive therapy =\< 7 days prior to registration
* Known history of active TB (Bacillus tuberculosis)
* Requires therapy with agents that have a predisposition for hepatoxicity
* Hypersensitivity to NVB or any of its excipients or to any component of AVD + BV therapy
* Requires immunosuppressive doses of corticosteroid therapy (\> 10 mg/day prednisone equivalents) for \>= 2 weeks prior to registration
* Active, known, or suspected autoimmune disease that requires systemic treatment (i.e. with use of disease modifying agents, corticosteroids or immunosuppressive drugs); Note: Replacement therapy (eg, thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment; subjects are permitted to enroll if they have vitiligo, type I diabetes mellitus, residual hypothyroidism due to autoimmune condition only requiring hormone replacement, psoriasis not requiring systemic treatment, or conditions not expected to recur in the absence of an external trigger
* Active infection requiring systemic IV antibiotic therapy
* History of Steven's Johnson's syndrome, toxic epidermal necrolysis syndrome (TENs) or motor neuropathy
* History or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the trial, interfere with the subject's participation for the full duration of the trial, or is not in the best interest of the subject to participate, in the opinion of the treating investigator
* Known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial
* Received prior therapy with an anti-PD-1, anti-PD-L1, or anti-PD-L2 agent
* Known history of human immunodeficiency virus (HIV) (HIV 1/2 antibodies)
* Known active hepatitis B (e.g., hepatitis B surface antigen \[HBsAg\] reactive) or hepatitis C (e.g., hepatitis C virus \[HCV\] ribonucleic acid \[RNA\] \[qualitative\] is detected)
* Received a live vaccine =\< 30 days prior to registration; Note: Seasonal influenza vaccines for injection are generally inactivated flu vaccines and are allowed; however, intranasal influenza vaccines (e.g., Flu-Mist) are live attenuated vaccines, and are not allowed; routine vaccinations, including seasonal influenza, must be given \>= 2 weeks prior to registration
* History of allergies and adverse drug reaction to study drug components
* History of another primary malignancy that has not been in remission for at least 3 years; (Note: The following are exempt for the 3-year limit: nonmelanoma skin cancer, fully excised melanoma in situ \[stage 0\], curatively treated localized prostate cancer, and cervical carcinoma in situ on biopsy or a squamous intraepithelial lesion on papanicolaou \[PAP\] smear)
* 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
* 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
* Receiving any other investigational agent which would be considered as a treatment for the primary neoplasm
* History of progressive promyelocytic leukemia (PML), known history of pancreatitis, active grade 3 or higher viral, bacterial or fungal infection =\< 2 weeks prior to registration and documented history of cerebrovascular event (stroke or transient ischemic attack \[TIA\]) =\< 6 months prior to registration