Inclusion Criteria:

- Patients must have a histologically confirmed solid malignancy, lymphoma, or multiple
myeloma for which standard curative or palliative measures do not exist, are no
longer effective, or for which the patient is not eligible or refuses (Phase I)

- Patients must have a histologically confirmed CD-20 positive B-cell non-Hodgkin
lymphoma for which standard curative or palliative measures do not exist, are no
longer effective, or for which the patient is not eligible or refuses (Phase Ib
cohort expansion)

- Patients must have histologically or cytologically confirmed marginal zone B-cell
lymphoma, small lymphocytic lymphoma, lymphoplasmacytic lymphoma, or mantle cell
lymphoma, and must have at least one measurable site of disease (phase II)

- For lymphoma and multiple myeloma patients: patients who have relapsed or are
refractory to at least one prior chemotherapeutic regimen or biologic agent; patients
must either be ineligible for or have refused curative options for treatment,
including stem cell transplant, if applicable

- For solid tumor patients: relapsed or refractory to at least one prior
chemotherapeutic regimen or biologic agent; patients must either be ineligible for or
have refused curative options for treatment

- Patients must have had a rest period of at least 2 weeks since prior chemotherapy or
radiation therapy, 6 weeks if the last regimen included BCNU or mitomycin C; there
must be a rest period of at least 3 months if the last therapy was immunotherapy or
radioimmunotherapy (unless the disease has progressed since treatment)

- ECOG performance status 0-1 (Karnofsky >= 60%)

- Life expectancy of greater than 3 months

- ANC ≥ 1,000/mcL

- Platelet count ≥ 100,000/mcL unsupported by transfusion within the prior 2 weeks

- Hemoglobin >= 8.0 g/dL unsupported by transfusion within the prior 2 weeks

- Total bilirubin =< 2x upper normal institutional limits; in patients with Gilbert's
disease or documented liver metastases, total bilirubin up to 3x ULN will be allowed

- AST(SGOT)/ALT(SGPT) ≤ 2.5 X institutional upper limit of normal

- Creatinine within normal institutional limits OR creatinine clearance >= 60
mL/min/1.73 m^2 for patients with creatinine levels above institutional normal

- Prior stem cell transplant allowed provided patient has not relapsed or progressed
within 100 days post transplant

- Women of child-bearing potential and men must agree to use adequate contraception
(hormonal, barrier method of birth control, or abstinence) prior to study entry and
for the duration of study participation

- Ability to understand and the willingness to sign a written informed consent document

- Toxicities from prior therapies must have resolved to baseline, or be =< grade 2 and
stable for at least one month

- Patient must be able to swallow pills

- Patients with CNS metastases must be stable after therapy for > 3 months and off
steroid treatment prior to study enrollment

Exclusion Criteria:

- Patients who have had chemotherapy or radiotherapy within 2 weeks (6 weeks for
nitrosoureas or mitomycin C) prior to entering the study or those who have not
recovered to baseline (or are not at stable grade =< 2) from adverse events due to
agents administered more than 2 weeks earlier; patients who have received
immunotherapy or radioimmunotherapy within 3 months, unless disease has progressed
since treatment; patients who have been administered ABT-888 as part of a single or
limited dosing study, such as a phase 0 study, will not be excluded from
participating in this study solely because of receiving prior ABT-888

- Patients may not be receiving any other investigational agents

- History of allergic reactions attributed to compounds of similar chemical or biologic
composition to ABT-888, bendamustine or mannitol; patients enrolling in the cohort
expansion or phase 2 portions of the study who have been intolerant of repeated doses
of rituximab in the past will be excluded (patients who have had infusion reactions
to their initial dose of rituximab will not be excluded)

- 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

- Pregnant women are excluded from this study because ABT-888 is a PARP inhibitor 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 ABT-888, breastfeeding should be discontinued if the mother is
treated with ABT-888; teratogenic and nonteratogenic events have been observed in
animal studies following intraperitoneal dosing of bendamustine

- HIV-positive patients on combination antiretroviral therapy are eligible if their HIV
is under adequate control with an antiretroviral regimen that has been stable for >=
4 weeks, as long as the CD4 count is > 300; appropriate studies will be undertaken in
patients receiving combination antiretroviral therapy when indicated; due to toxicity
issues, patients on zidovudine or stavudine would not be eligible

- Patients with history of seizure are not eligible

- Patients with uncontrolled CNS metastasis are not eligible

- Patients with unrelated prior malignancies must have undergone potentially curative
therapy for their prior malignancy, have no evidence of that disease for three years,
and be deemed at low risk for recurrence of their prior malignancy by her/his
treating physician; patients with dermal squamous cell carcinoma, basal cell
carcinoma or melanoma in situ that has been completely excised will be eligible
following excision

- Patients with active seizure or a history of seizure