Dalteparin and Sunitinib Malate as First-Line Therapy in Treating Patients With Kidney Cancer That is Metastatic or Cannot Be Removed by Surgery

Inclusion Criteria: * Patients must have histologically confirmed renal cell carcinoma that is metastatic or unresectable * Renal carcinoma patients with predominant clear-cell histology are eligible; papillary renal cell carcinoma, oncocytoma, collecting duct tumors and transitional cell carcinoma are NOT eligible * No prior systemic treatments for metastatic disease are permitted, including antiangiogenic therapy, immunotherapy, chemotherapy and investigational therapy * Prior palliative radiation to metastatic lesion(s) is permitted, provided there is at least one measurable and/or evaluable lesion(s) that has not been irradiated * Radiation therapy must be completed \> 4 weeks prior to registration * Patients must have measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension as \>= 20 mm with conventional techniques or as approximately \>= 10 mm with spiral computed tomography (CT) scan (Response Evaluation Criteria in Solid Tumors \[RECIST\] 1.0 criteria) * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 * Leukocytes \> 3,000/mm\^3 * Absolute neutrophil count \> 1,500/mm\^3 * Platelets \> 100,000/mm\^3 * Total bilirubin \< 1.5 x laboratory upper limit of normal (ULN) * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/ alanine transaminase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) \< 2.5 x laboratory ULN * Creatinine \< 1.5 x laboratory ULN * Prothrombin time (PT)/international normalized ratio (INR) \< 1.5 * Urine protein \< 1+; if \> 1+, 24 hour urine protein should be obtained and should be \< 1000 mg * Women of child-bearing potential must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation * Should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately * Ability to understand and the willingness to sign a written informed consent document * Except for Dalteparin that will be administered as a study drug, the patients should not take any other anticoagulants or antiplatelet agents during the study, including but not limited to nonsteroidal anti-inflammatory drugs (NSAID) (any dose of aspirin), warfarin or other anticoagulants Exclusion Criteria: * Patients may not be receiving any other investigational agents * Patients with known central nervous system (CNS) metastases; patients should have a head CT/magnetic resonance imaging (MRI) within 4 weeks prior to treatment initiation; any imaging abnormality indicative of CNS metastases will exclude the patient from the study * Patients with a "currently active" second malignancy other than non-melanoma skin cancers are not eligible; patients are not considered to have a "currently active" malignancy if they have completed anti-cancer therapy and are considered by their physician to be at less than 30% risk of relapse * Patients with a large (\> 2 cm) pulmonary lesion involving the trachea or one of the main bronchus and any endobronchial lesion * History of allergic reactions attributed to compounds of similar chemical or biologic composition to dalteparin * Evidence of bleeding diathesis within last 6 months * Serious or non-healing wound, ulcer or bone fracture or active peptic ulceration * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure (New York Association class II, III, or IV), angina pectoris requiring nitrate therapy, recent myocardial infarction (\< the last 6 months), cardiac arrhythmia, history of cerebrovascular accident (CVA) within 6 months (thrombotic or hemorrhagic), hypertension (defined as blood pressure of \> 160 mmHg systolic and/or \> 90 mm Hg diastolic on medication), hemorrhagic retinopathy, history of peripheral vascular disease, or psychiatric illness/social situations that would limit compliance with study requirements * Patients with an ejection fraction \< 50% by multi gated acquisition scan (MUGA) scan are not eligible * Pregnant women are excluded from this study * History of abdominal fistula, gastrointestinal perforation or intra-abdominal abscess within 28 days prior to day 1 therapy * Invasive procedures defined as: * Major surgical procedure, open biopsy, or significant traumatic injury within 6 weeks prior to day 1 therapy * Anticipation of need for major surgical procedures during the course of the study * Core biopsy within 7 days prior to start therapy