Safety Study of ABT-263 in Combination With Rituximab in Lymphoid Cancers

Inclusion Criteria: * Diagnosed with a CD20-positive lymphoproliferative disorder (Revised European American Lymphoma \[REAL\]/World Health Organization \[WHO\]) and bi-dimensionally measurable disease with at least 1 lesion \>= 1.0 cm * Eastern Cooperative Oncology Group (ECOG) performance score of \<= 1 * Adequate bone marrow function, independent of growth factor support (with the exception of participants with bone marrow that is heavily infiltrated with underlying disease \[80% or more\] who may use growth factor to achieve Absolute Neutrophil count (ANC) eligibility criteria) per local laboratory reference range as follows: Absolute Neutrophil count (ANC) \>= 1000/μL; Platelets \>= 100,000/mm3 (untransfused); Hemoglobin \>= 9.0 g/dL. * Participants who have a history of autologous stem cell transplant (e.g., bone marrow) must be \> 6 months post transplant and have adequate bone marrow function, independent of any growth stimulating factors (with the exception of participants with bone marrow that is heavily infiltrated with underlying disease \[80% or more\] who may use growth factor to achieve ANC eligibility criteria) per local laboratory reference range as follows: Absolute Neutrophil count (ANC) \>= 1500/μL; Platelets \>= 125,000/mm3 (untransfused); Hemoglobin \>= 10.0 g/dL. * Participant must have adequate renal, hepatic and coagulation function per local laboratory reference range as follows: Serum creatinine \<= 2.0 mg/dL or calculated creatinine clearance \>= 50 mL/min; AST and ALT \<= 3.0 × the upper normal limit (ULN); Bilirubin \<= 1.5 × ULN. Participants with Gilbert's Syndrome may have a Bilirubin \> 1.5 × ULN; activated partial thromboplastin time (aPTT), prothrombin time (PT) not to exceed 1.2 × ULN * Females must be surgically sterile, postmenopausal (at least 1 year), or have negative pregnancy test at screening on serum sample obtained within 14 days prior to initial study drug administration, and prior to dosing on a urine obtained on Lead-in Day 1, if it has been \> 7 days since obtaining the serum pregnancy test results. Females not surgically sterile or postmenopausal (at least 1 year) and non-vasectomized males must practice at least 1 of the following: total abstinence from sexual intercourse (minimum 1 complete menstrual cycle),a vasectomized partner, hormonal contraceptives for at least 3 months prior to study drug administration, or double-barrier method. Inclusion Criteria (Extension Study) Participants who enter the Extension Study must continue to meet all Inclusion and Exclusion criteria, with the exception of inclusion criteria regarding measurable disease and inclusion criteria regarding laboratory parameters. Participants entering the Extension Study must also have stable lab values per local laboratory reference ranges. In addition they must meet the following lab criteria: * Participants must meet the following hematology and coagulation lab criteria: * Platelet counts must be \>= 25,000/mm3 (untransfused). Platelet counts \<= 50,000/mm3 must be stable and monitored at an increased frequency at the discretion of the investigator. * Absolute Neutrophil count (ANC) \>= 500/μL. ANC \>= 500/μL and \< 1,000/μL should be monitored at an increased frequency at the discretion of the investigator. * Hemoglobin of \>= 8.0 g/dL. * aPTT, PT is not to exceed 1.2 × ULN. * Participants' chemistry values must not exceed Grade 2. Grade 2 chemistry labs should be monitored at an increased frequency at the discretion of the investigator. Participants must meet the following chemistry criteria: * Serum creatinine \<= 3.0 × the upper normal limit (ULN) of institution's normal range. * AST and ALT \<= 5.0 × the upper normal limit (ULN) of institution's normal range. * Bilirubin \<= 3 × ULN. Participants with Gilbert's Syndrome may be allowed to have a Bilirubin \> 3 × ULN based on a joint decision between the investigator and AbbVie medical monitor. Exclusion Criteria: * History of or clinically suspicious for cancer-related Central Nervous System (CNS) disease, allogeneic stem cell transplant, recurrent significant infections, previous or current malignancies within the last 5 years (except: adequately treated in situ carcinoma of the cervix uteri; basal or squamous cell carcinoma of the skin; in situ carcinoma of the bladder; previous malignancy confined and surgically resected with curative intent), toxicity from rituximab that resulted in permanent discontinuation of treatment or toxicity from ABT-263 or another Bcl-2 family protein inhibitor, significant cardiovascular disease (e.g., MI within 6 months), renal, neurologic, psychiatric, endocrinologic, metabolic, immunologic or hepatic disease that would adversely affect participation, severe (defined as Grade 4 and/or requiring permanent discontinuation of prior antibody therapy) allergic or anaphylactic reactions to human, humanized, chimeric or murine monoclonal antibodies * The participant has an underlying, predisposing condition of bleeding or currently exhibits signs of clinically significant bleeding. The participanthas a recent history of non-chemotherapy induced thrombocytopenic associated bleeding within six months prior to the first dose of study drug. The participant has active peptic ulcer disease or other hemorrhagic esophagitis/gastritis or active immune thrombocytopenic purpura (ITP) or a history of being refractory to platelet transfusions (within six months prior to the first dose of study drug). * Female participant is pregnant or breast-feeding * Participant has tested positive for HIV, Hepatitis B or Hepatitis C infection, (Participants who test positive for anti-HBc (carrier) will be allowed to enroll) * Evidence of other clinically significant uncontrolled condition(s) including, but not limited to: active systemic fungal infection; diagnosis of fever and neutropenia within one week prior to study drug administration * Received steroid therapy for anti-neoplastic intent within seven days prior to the first dose of study drug,received aspirin within seven days prior to the first dose of study drug, CYP3A inhibitors (e.g., ketoconazole, clarithromycin) within 7 days prior to the administration of the first dose of study drug, radio-immunotherapy within six months prior to first dose of study drug,received any anti-cancer therapy within fourteen days prior to the first dose of study drug.