Inclusion Criteria:

- Histologically or cytologically confirmed advanced, unresectable, or metastatic soft
tissue sarcoma (STS)

- Measurable disease, defined as >= 1 lesion that can be accurately measured in >= 1
dimension as >= 2 cm by conventional techniques OR >= 1 cm by spiral computed
tomography (CT) scan

- No small round cell tumors, including the following:

- Primitive neuroectodermal tumor

- Rhabdomyosarcoma

- Ewing sarcoma

- Osteosarcoma

- No known active and/or untreated brain metastases and/or brain metastases requiring
ongoing therapy (e.g., corticosteroids)

- Treated, inactive brain metastases not requiring ongoing therapy allowed
provided the brain metastases have been stable for >= 1 month as assessed by
intracranial imaging AND there is no indication of increased vascularity of the
treated metastases within 14 days before study entry as assessed by magnetic
resonance imaging (MRI)

- Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0-1 OR Karnofsky PS
70-100%

- Life expectancy >= 12 weeks

- Absolute neutrophil count (ANC) >= 1,500/mm^3

- Platelet count >= 100,000/mm^3

- Total bilirubin normal

- Aspartate aminotransferase (AST) and/or alanine aminotransferase (ALT) =< 2.5 times
upper limit of normal

- Creatinine normal OR creatinine clearance >= 60 mL/min

- Not pregnant or nursing

- Negative pregnancy test

- Fertile patients must use effective contraception

- Able to take oral medication

- No peripheral neuropathy >= grade 2

- No concurrent uncontrolled illness including, but not limited to, any of the
following:

- Ongoing or active infection

- Symptomatic congestive heart failure

- Unstable angina pectoris

- Cardiac arrhythmia or myocardial infarction within the past 6 months

- Psychiatric illness and/or social situation that would limit compliance with
study requirements

- No history of Torsades de Pointes

- No history of allergic reactions attributed to compounds of similar chemical or
biological composition to vorinostat or bortezomib

- No more than 1 prior systemic treatment for advanced STS, including investigational
agents

- Adjuvant therapy is not considered a systemic regimen

- More than 2 weeks since prior valproic acid

- More than 4 weeks since prior and no concurrent chemotherapy (> 6 weeks for
nitrosoureas or mitomycin C) or radiotherapy and recovered

- Radiotherapy to bone metastasis within the past 2 weeks allowed provided there
is active non-bone disease outside the radiation port

- No prior radiotherapy to >= 33% of the bone marrow

- No prior vorinostat or bortezomib

- No concurrent category I medications that are generally accepted to have a risk of
causing Torsades de Pointes, including any of the following:

- Quinidine, procainamide, disopyramide

- Amiodarone, sotalol, ibutilide, dofetilide

- Erythromycin, clarithromycin

- Chlorpromazine, haloperidol, mesoridazine, thioridazine, pimozide, cisapride,
bepridil, droperidol, methadone, arsenic, chloroquine, domperidone,
halofantrine, levomethadyl, pentamidine, sparfloxacin, lidoflazine

- No concurrent combination antiretroviral therapy for human immunodeficiency virus
(HIV)-positive patients

- No other concurrent investigational agents for the primary malignancy

- No other concurrent anticancer therapy