Naproxen in Preventing DNA Mismatch Repair Deficient Colorectal Cancer in Patients With Lynch Syndrome

Inclusion Criteria: * Participants must have Lynch syndrome defined as meeting any of the following: * "Mutation-positive Lynch syndrome": carriers or obligate carriers (by pedigree) of a pathogenic mutation in one of the DNA mismatch repair (MMR) genes (i.e. mutL homolog 1 \[MLH1\], mutS homolog 2 \[MSH2\]/epithelial cell adhesion molecule \[EPCAM\], mutS homolog 6 \[MSH6\], or PMS2 postmeiotic segregation increased 2 \[S. cerevisiae\] \[PMS2\]) or * "Mutation-negative Lynch syndrome": patients with a personal history of a non-sporadic MMR deficient premalignant lesion (i.e. polyp) or a non-sporadic MMR deficient malignant tumor (where "non-sporadic MMR deficient" is defined by: microsatellite-instability high by either immunohistochemistry or microsatellite instability \[MSI\] testing or both, but no evidence of MLH1 promoter methylation in cases with loss of both MLH1 and PMS2, and/or no evidence of v-raf murine sarcoma viral oncogene homolog B \[BRAF\] mutation in cases with loss of both MLH1 and PMS2) but germline MMR genetic testing showed either a variant of unknown significance or mutation negative result or had declined germline MMR genetic testing * Participants must not have evidence of active/recurrent malignant disease for 6 months * Participants must be at least 6 months from any prior cancer-directed treatment (such as surgical resection, chemotherapy, immunotherapy, hormonal therapy or radiation) * Participants must have endoscopically accessible distal colon and/or rectal mucosa (i.e. participants must have at least part of the descending/sigmoid colon and/or rectum intact) * Participants must consent to one standard of care lower gastrointestinal (GI) endoscopy (flexible sigmoidoscopy or colonoscopy) with biopsies and one flexible sigmoidoscopy with biopsies that will be 6 months (+14 days) apart * Participants must consent to refrain from using aspirin or non-steroidal anti-inflammatory drugs (NSAIDs) or cyclooxygenase (COX)-inhibitors for the duration of the trial * Eastern Cooperative Oncology Group (ECOG) performance status =\< 1 (Karnofsky \>= 70%) * Hemoglobin \>= 10 g/dL or hematocrit \>= 30% * Leukocyte count \>= 3,000/microliter * Platelet count \>= 100,000/microliter * Absolute neutrophil count \>= 1,500/microliter * Creatinine =\< 1.5 x institutional upper limit of normal (ULN) (OR glomerular filtration rate \[GFR\] \> 30 ml/min/1.73 m\^2) * Total bilirubin =\< 2 x institutional ULN * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\]) =\< 2.5 x institutional ULN * Alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 x institutional ULN * The effects of naproxen on the developing human fetus at the recommended therapeutic dose are unknown; for this reason and because NSAIDs are known to be teratogenic, women of child-bearing potential must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) for the duration of study participation; should a woman become pregnant or suspect she is pregnant at the time of study entry or while participating in this study, she should inform her study physician immediately; women of childbearing potential must agree to baseline and pre-drug pregnancy tests * Ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * Individuals who received scheduled aspirin, NSAIDs, or COX-inhibitors of any kind for more than 3 days (\> 3 days) during anytime within the 2 weeks preceding baseline eligibility screening visit; individuals on cardio-protective aspirin will not be eligible * Individuals who are status post total proctocolectomy (i.e. removal of all colon and rectum) * Individuals with active gastroduodenal ulcer disease in the preceding 5 years * Individuals with any history of transfusion-dependent gastrointestinal bleeding, gastrointestinal perforation or gastrointestinal obstruction; if any of these events had been due to a malignancy of the GI tract and the malignancy has since been removed, the patient is eligible * Individuals with history of myocardial infarction, stroke, coronary-artery bypass draft, invasive coronary revascularization in the preceding 5 years * Individuals taking the drugs listed below may not be randomized unless they are willing to stop the medications (and possibly change to alternative non-excluded medications to treat the same conditions) no less than 7 days prior to starting naproxen or placebo on this study; consultation with the participant's primary care provider may be obtained but is not required; the use of the following drugs or drug classes is prohibited during naproxen/placebo treatment: * Investigational agents * NSAIDs: such as aspirin, ketorolac and others NSAIDs * COX-2 inhibitors: such as celecoxib, rofecoxib and other COX-2 * Antiplatelet agents: such as aspirin, clopidogrel, ticlopidine, dipyridamole, abciximab, tirofiban, eptifibatide and prasugrel * Anticoagulants: * Heparin * Heparinoids: such as fondaparinux, danaparoid and other heparinoids * Low-molecular weight heparins: such as enoxaparin, dalteparin, parnaparin, reviparin, tinzaparin, ardeparin, certoparin, lepirudin, bivalirudin * Other anticoagulants: argatroban, apixaban, dabigatran, rivaroxaban, warfarin, acenocoumarol, dicumarol, phenindione and other anticoagulants * Lithium * Selective serotonin and norepinephrine reuptake inhibitors: milnacipran, fluoxetine, paroxetine, nefazodone, citalopram, clovoxamine, escitalopram, flesinoxan, femoxetine, duloxetine, venlafaxine, vilazodone, sibutramine, desvenlafaxine * Anticonvulsants: phenytoin, paraldehyde, valproic acid, carbamazepine, trimethadione, phenobarbital, diazepam, chlormethiazole, mephenytoin, ethotoin, paramethadione, phenacemide, mephobarbital, oxcarbazepine, zonisamide, piracetam, vigabatrin, felbamate, gabapentin, beclamide, fosphenytoin, stiripentol, tiagabine, topiramate, pregabalin, lacosamide, rufinamide, caramiphen * Antibiotics and antifungals: * Fluoroquinolones : such as ofloxacin, norfloxacin, levofloxacin * Other agents: teriflunomide, cyclosporine, tacrolimus, ginkgo, gossypol, meadowsweet, feverfew, beta glucan, pentosan, pentoxifylline, cilostazol, erlotinib, pemetrexed, methotrexate, pralatrexate * Individuals with uncontrolled renal insufficiency or renal failure * History of allergic reactions attributed to naproxen * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, uncontrolled hypertension, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements * Pregnant, breast-feeding, or women of childbearing potential unwilling to use a reliable contraceptive method; pregnant women are excluded from this study because naproxen/NSAIDs is an agent with the potential for teratogenic or abortifacient effects; because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with naproxen, breastfeeding should be discontinued if the mother is treated with naproxen