Surgery in Treating Patients With Early Stage Anal Canal or Perianal Cancer and HIV Infection

Inclusion Criteria: * A single, biopsy-proven SISCCA as defined by the LAST criteria (=\< 3mm depth of invasion, horizontal spread of =\< 7 mm, and completely excised with at least 1 mm margin clear of cancer irrespective of the amount of HSIL) documented per investigator assessment in combination with the pathology report within 12 months before Segment B enrollment. * No evidence of any lymph node spread or distant metastases as determined by PET CT imaging within 16 weeks before Segment B enrollment. Alternatively, for those without PET CT capability, an MRI or CT of the abdomen and pelvis and a chest x-ray confirming no evidence of metastatic disease is acceptable. * Clinician believes that eradication of concomitant HSIL is reasonable and feasible based on the extent of disease and overall medical condition of the subject * HIV-1 infection, as documented by one of the following: licensed HIV screening (antibody and/or HIV antibody/antigen combination assay confirmed by a second licensed HIV assay such as a HIV-1 Western blot confirmation or HIV rapid multispot antibody differentiation assay, Documentation of HIV diagnosis in the medical record by a licensed HIV rapid test health care provider, HIV-1 RNA detection by a licensed HIV-1 RNA assay demonstrating \>1000 RNA copies/mL, or Documentation of receipt of ART by a licensed health care provider. * Prior to Segment B enrollment, patients on combination anti-retroviral therapy (cART) will be required to have a minimum cluster of differentiation (CD)4 count of \>= 200 and patients not on cART will be required to have a minimum CD4 count of \>=350 to be eligible for the study; patients not currently on cART who have a CD4 count \> 200 and who agree to start cART immediately will be eligible for participation; laboratory data should be obtained within 16 weeks prior to Segment B enrollment * Participants must have Eastern Cooperative Oncology Group (ECOG) performance status 0-2 * Participants must have a life expectancy of 2 years or more * Participants must not have any other concurrent malignancy * Participants must be age 18 years old or older. * Leukocytes: \>= 3,000/mm\^3 * Absolute neutrophil count: \>= 1,500/mm\^3 * Platelets: \>= 100,000/mm\^3 * Women of childbearing potential must have a negative urine pregnancy test within 7 days prior to randomization enrollment; female participants enrolled in the treatment arm are advised to not become pregnant during study participation; all women of childbearing potential must agree to either commit to continued abstinence from heterosexual intercourse or use a reliable birth control method (oral contraceptive pills, intrauterine device, Nexplanon, DepoProvera, or bilateral tubal ligation, etc., or another acceptable method as determined by the investigator) during the entire period of the trial (5 years or more), and must not intend to become pregnant during study participation and for 3 months after treatment is discontinued if the participant is enrolled in the treatment arm. * Men should not father a child while in this study; men who could father a child must agree to use at least one form of birth control or continued abstinence from heterosexual intercourse if receiving topical treatment during during the study and for 2 weeks after stopping topical treatment * Participants must be able to understand and willing to sign a written informed consent document * Participants must, in the opinion of the Investigator, be capable of complying with the requirements of this protocol Exclusion Criteria: * Anal cancer that cannot be completely excised with a \>=1 mm clear margin from surrounding tissue or where excision to obtain a clear margin would compromise sphincter function or anal canal diameter * Concurrent anal canal or perianal HSIL or condyloma that in the judgment of the clinician cannot be cleared or can only be cleared with undue morbidity to the patient * No prior history of anal cancer, including SISCCA * Ongoing use of anticoagulant therapy other than aspirin or non-steroidal anti-inflammatory drugs (NSAIDS) that cannot be stopped for surgical procedures * Acute treatment for an infection (excluding fungal infection of the skin and sexually transmitted infections) or other serious medical illness within 2 weeks before enrollment * Current systemic chemotherapy or radiation therapy that potentially causes bone marrow suppression that would preclude safe treatment of HSIL; Note: Kaposi's sarcoma limited to the skin is not exclusionary unless requiring systemic chemotherapy * The participant's SISCCA must not have been ablated. * Participants who are receiving any other investigational agents within 4 weeks prior to enrollment. Investigational antiretroviral agents for HIV are acceptable. * Participant plans to relocate away from the study site during study participation.