Letrozole in Preventing Breast Cancer in Healthy Postmenopausal Women at High Risk for Breast Cancer

Inclusion Criteria: * Healthy postmenopausal women at "high risk" for breast cancer will be eligible for the study; definition of menopause will be: * Amenorrhea for at least 12 months, or * History of hysterectomy and bilateral salpingo-oophorectomy, or * At least 55 years of age with prior hysterectomy with or without oophorectomy, or * Age 35 to 54 with a prior hysterectomy without oophorectomy OR with a status of ovaries unknown with documented follicle-stimulating hormone level demonstrating elevation in postmenopausal range * "High risk" for breast cancer will be defined as: * Prior histologically confirmed lobular carcinoma in situ (LCIS) treated by local excision only, or * At least 1.66% probability of invasive breast cancer within 5 years using the Breast Cancer Risk Assessment Tool * Eastern Cooperative Oncology Group (ECOG) performance status 0 or 1; Karnofsky 80% or above * Leukocytes \>= 3,000/uL * Absolute neutrophil count \>= 1,500/uL * Platelets \>= 100,000/uL * Total bilirubin =\< 2.0 mg/dL * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.0 X institutional ULN * Creatinine =\< 1 X institutional ULN * Recent mammogram negative for breast cancer, Breast Imaging-Reporting and Data System (BIRADS) score \< 3 (within the last 12 months) * Ability to understand and the willingness to sign a written informed consent document; only potential participants with the ability to understand and the willingness to sign a written document will be presented with an informed consenting document Exclusion Criteria: * Women diagnosed with osteoporosis (previously or on screening dual-energy X-ray absorptiometry \[DEXA\] for this study) and not on a stable dose of long or short-acting bisphosphonates therapy for at least 3 months will be excluded from the study; women diagnosed with osteoporosis and on raloxifene (Evista) therapy will be excluded from the study; use of calcium and/or vitamin D for osteoporosis prevention or treatment is allowed; women with osteopenia will be allowed to participate in this study * Have had invasive cancer within the past five years except non-melanoma skin cancer * Evidence of suspicious of malignant disease on bilateral mammogram within the past year unless ruled out by further evaluation * History of prior invasive breast cancer or intraductal carcinoma in situ, or history of prior radiation therapy to the chest or breast * Participants may not be receiving any other investigational agents; participants may not be concurrently enrolled in another breast cancer prevention intervention trial * History of allergic reactions attributed to compounds of similar chemical or biologic composition to letrozole * 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 * Within 3 months since prior estrogen or progesterone replacement therapy, oral contraceptives, androgens, luteinizing hormone-releasing hormone analogs, prolactin inhibitors, or antiandrogens * Within 3 months since prior tamoxifen, raloxifene, or other selective estrogen-receptor modulators * Within 3 months since regular use (more than 2 times a week) of prior estrogenic supplements or herbal remedies * History of bleeding or clotting disorder; current or recent (within 3 months) use of Coumadin, Plavix or other systemic anticoagulant other than aspirin is not permitted if subject chooses to participate in the optional RPFNA procedure; if a subject chooses not to participate in the RPFNA procedure, prior or current treatment with systemic anticoagulants is permitted