This phase II trial is studying how well giving bendamustine hydrochloride, etoposide, dexamethasone, and filgrastim together for peripheral stem cell mobilization works in treating patients with refractory or recurrent lymphoma or multiple myeloma. Giving chemotherapy, such as bendamustine hydrochloride, etoposide, and dexamethasone, before a peripheral stem cell transplant stops the growth of cancer cells by stopping them from dividing or killing them. Giving colony-stimulating factors, such as filgrastim, and certain chemotherapy drugs helps stem cells move from the bone marrow to the blood so they can be collected and stored