ShortStop-HER2: 12 Months vs. 6 Months of HER2-targeted Medications for People With HER2+ Breast Cancer Who Had a Pathologic Complete Response After Chemotherapy Plus Trastuzumab

Inclusion Criteria: * Patients (females and males) with clinical stage T1c-T3 (or Tx) and nodal stage N0-N1 (except T3N1 tumors, which are not eligible) * Patients must have no residual invasive disease in the breast or lymph nodes after the completion of neoadjuvant therapy. Residual ductal carcinoma in situ (DCIS) is allowed. Patients with residual isolated tumor cells at surgery are considered node-positive and are not eligible * HER2+ by American Society of Clinical Oncology (ASCO)/College of American Pathologists (CAP) guidelines. Central pathology review is not required. In cases where there were multiple tumor sites in breast/nodes that had HER2 testing at diagnosis, at least one site must have been HER2+ AND the treating investigator must feel it is in the patient's best interest to be treated as having HER2+ breast cancer * Known hormone receptor status as defined by ASCO/CAP guidelines. Estrogen receptor (ER) and progesterone receptor (PR) of any values are allowed. Hormone receptor positive status can be determined by either known positive ER or known positive PR status; hormone receptor negative status must be determined by both known negative ER and known negative PR * If invasive disease was present in both breasts, participation in the study is permitted as long as the eligibility criteria are met for both tumors/breasts (including the requirement that at least one biopsied site on each side must have been HER2+) * Age ≥ 18 years * Eastern Cooperative Oncology Group (ECOG) performance status 0-2 * Patients must have received neoadjuvant chemotherapy in combination with trastuzumab with or without pertuzumab for a minimum of 12 weeks. All chemotherapy must have been completed preoperatively * Patient must complete a minimum of 12 weeks of coverage with trastuzumab and a maximum of 24 weeks in the combined neoadjuvant and adjuvant setting prior to trial registration. Trastuzumab may have been administered either weekly or once every 3 weeks (q3weeks). (For purposes of this eligibility criterion, a single dose of q3week trastuzumab would provide 3 weeks of coverage; a single dose of once a week (q1week) trastuzumab would provide 1 week of coverage. If a q3week dose of trastuzumab were administered and then the subsequent dose was delayed for any period of time, that would still count as 3 weeks of coverage.) * Administration of endocrine therapy for treatment of this breast cancer is allowed prior to trial registration. If a patient received prior breast cancer endocrine therapy (eg tamoxifen or aromatase inhibitor) for DCIS or preventive indication, and endocrine therapy is indicated for treatment of their current breast cancer, then prior endocrine therapy must have been stopped \> 12 months prior to registration on this protocol * No use of investigational anti-cancer agents at time of registration * Patient must register within 14 weeks of final surgery * Adequate excision: Surgical removal of all clinically evident disease in the breast and lymph nodes as follows: * Breast surgery: Total mastectomy with grossly negative margins (in the opinion of the surgeon there is no disease grossly at the margins) or breast-conserving surgery with histologically negative margins (no ink on tumor, including DCIS) unless those margins are anterior at the skin or posterior at the chest wall and no additional margin re-excision can be performed * Lymph node surgery: Lymph node surgery must have been performed and can include sentinel lymph node biopsy, targeted axillary dissection, or axillary dissection, at the discretion of the breast surgeon * Adequate radiation: Patients who completed breast-conserving surgery (i.e. lumpectomy) must have received or plan to receive adjuvant radiation. If breast-conserving surgery was performed but patient will not be receiving breast radiation, the patient is not eligible. Patients for whom radiotherapy would be recommended for breast cancer treatment but for whom it is contraindicated because of medical reasons (e.g., connective tissue disorder or prior ipsilateral breast radiation) are not eligible * Adjuvant radiation can be given on study, and in this case is encouraged to be given concurrently with adjuvant HER2-directed therapy, per investigator discretion * Targeting of the regional nodal basins will be at treating investigator discretion * Not pregnant and not nursing, because this study involves agents with known teratogenic potential. Therefore, for women of childbearing potential only, a negative serum or urine pregnancy test should be performed prior to receiving HER2-directed therapy according to local standard practice * Adequate hepatic, renal and bone marrow function to receive adjuvant HER2-directed therapy in the opinion of the treating investigator. There are no specific required laboratory values for eligibility * No stage IV (metastatic) breast cancer * 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 * No history of any prior (ipsilateral \[ipsi-\] or contralateral) invasive breast cancer. Prior DCIS is allowed * No evidence of recurrent disease following preoperative therapy and surgery * Patients living with HIV who are healthy and deemed by their medical team to have a low risk of AIDS-related illnesses are included in this trial. Patients with Hepatitis B or Hepatitis C virus who are healthy and deemed by their medical team to meet all other enrollment criteria are included in this trial. * Patients with inadequate cardiac function on most recent assessment of left ventricular ejection fraction (LVEF) are not eligible for this trial. Inadequate cardiac function is defined as LVEF \< 50% on echocardiogram (echo) or multiple-gated acquisition (MUGA) * No history of grade 3 or 4 toxicity related to trastuzumab. If pertuzumab is planned to be