Inclusion Criteria:

* Patients must have confirmation of DT/DF by local pathologist prior to registration
* Patients may have been treated with locoregional therapies such as major surgery, radiation, radiofrequency ablation, or cryosurgery provided this has been completed at least 4 weeks prior to registration and recovered from therapy related toxicity to less than CTCAE grade 2
* Patients may have been treated with cytotoxic, biologic (antibody), immune or experimental therapy, tyrosine kinase inhibitors, hormone inhibitors or nonsteroidal anti-inflammatory drugs (NSAIDs) provided this has been completed at least 4 weeks prior to registration (6 weeks for mitomycin and nitrosoureas) and recovered from any therapy related toxicity to less than CTCAE grade 2
* Patients with prior or current treatment of sorafenib are excluded
* No concomitant treatment, in therapeutic doses, with anticoagulants such as warfarin or warfarin-related agents, heparin, thrombin or Factor Xa inhibitors, or antiplatelet agents (e.g., clopidogrel); low dose aspirin (=\< 81 mg/day), low-dose warfarin (=\< 1 mg/day), and prophylactic low molecular weight heparin (LMWH) are permitted; please note that drugs that strongly induce or inhibit cytochrome P450, family 3, subfamily A, polypeptide 4 (CYP3A4) or are associated with a risk of torsades are not allowed; chronic concomitant treatment of CYP3A4 inducers is not allowed (e.g., dexamethasone, phenytoin, carbamazepine, rifampin, rifabutin, rifapentin, phenobarbital, and St. John's wort); as part of the enrollment/informed consent procedures, the patient will be counseled on the risk of interactions with other agents, and what to do if new medications need to be prescribed or if the patient is considering a new over-the-counter medicine or herbal product; the following drugs are strong inhibitors of CYP3A4 and are not allowed during the treatment with sorafenib:

* Boceprevir
* Indinavir
* Nelfinavir
* Lopinavir/ritonavir
* Saquinavir
* Telaprevir
* Ritonavir
* Clarithromycin
* Conivaptan
* Itraconazole
* Ketoconazole
* Mibefradil
* Nefazodone
* Posaconazole
* Voriconazole
* Telithromycin

* Drugs with possible or conditional risk of torsades should be used with caution knowing that sorafenib could prolong the QT interval
* Chronic daily NSAID use as treatment for controlling desmoid tumors is not allowed, and should be stopped \>= 3 days prior to registration; NSAIDS are allowed when used for desmoid tumor-related pain or for symptoms that are unrelated to desmoid disease (eg. headache, arthritis)
* Patients must have measurable disease
* Patients have to meet one of the following criteria to be eligible:

* Disease determined unresectable or entailing unacceptably morbid surgery based on 1 or more of the following characteristics:

* Multifocal disease
* Disease in which there is involvement or inadequate plane from: neurovascular bundle, bone, skin, or viscera
* Large size in relationship to location OR multi-compartment involvement
* Progression by radiographic imaging (10% increase in size by RECIST v1.1 within 6 months of registration)
* Patients with symptomatic disease which meets the following criteria Brief Pain Inventory (BPI) score greater than or equal to 3 AND one of the following:

* Inability to control pain with NSAIDs and considering addition of narcotics OR
* \> 30% increase in current use of narcotics OR
* Addition of a new opioid narcotic
* Eastern Cooperative Oncology Group (ECOG) performance status =\< 2
* Patients who are pregnant or nursing are not eligible
* No patients with a history of cardiac disease: congestive heart failure \> class II New York Heart Association (NYHA); active coronary artery disease (CAD) (myocardial infarction or unstable angina within 6 months prior to study entry)
* No patients with inadequately controlled hypertension (defined as a blood pressure of \>= 150 mmHg systolic and/or \>= 90 mmHg diastolic), or any prior history of hypertensive crisis or hypertensive encephalopathy
* No patients with clinically significant gastrointestinal (GI) bleeding or bleeding diathesis within 30 days prior to registration
* Absolute neutrophil count \>= 1,500/mm\^3
* Hemoglobin \>= 8 g/dl
* Platelets \>= 75,000/mm\^3
* Total bilirubin =\< 1.5 x upper limits of normal (ULN)
* Serum glutamic oxaloacetic transaminase (SGOT) (aspartate aminotransferase \[AST\])/serum glutamate pyruvate transaminase (SGPT) (aspartate aminotransferase \[ALT\]) =\< 1.5 x ULN
* Calculated creatinine clearance \>= 50 mL/min using the Cockcroft-Gault equation