Donor Natural Killer Cells, Cyclophosphamide, and Etoposide in Treating Children and Young Adults With Relapsed or Refractory Solid Tumors

Inclusion Criteria:

* SCREENING: Patients with relapsed or refractory solid tumors and without known curative therapy or therapy proven to proven to prolong survival with acceptable quality of life.
* SCREENING: Patients older than 21 years must have a solid tumor considered by study doctor to be of the childhood cancer type.
* SCREENING: Performance level as measured by Karnofsky \>= 60% for patients \> 16 years of age or Lansky \>= 60% for patients =\< 16 years of age.
* SCREENING: Documentation of measurable or evaluable non-measurable disease.
* SCREENING: At least one documented histological verification of solid tumor diagnosis. Can be from original diagnosis or more recent.
* ENROLLMENT: Patient must have fully recovered (i.e. returned to baseline) from the clinically significant acute treatment-related toxicities of all prior treatments prior to beginning treatment on this protocol with exceptions of cytopenias resulting from persistent disease, hearing loss and alopecia.
* ENROLLMENT: Performance level as measured by Karnofsky \>= 60% for patients \> 16 years of age or Lansky \>= 60% for patients =\< 16 years of age.
* ENROLLMENT: Creatinine clearance \>= 60 mL/min/1.73m\^2 (calculated by 24 hour \[h\] urine collection or nuclear glomerular filtration rate \[GFR\] scan if 24 h collection is not possible) or a serum creatinine based on age and gender as follows:

  * Age, maximum serum creatinine (mg/dL):

    * 1 month to \< 6 months, male 0.4, female 0.4;
    * 6 months to \< 1 year, male 0.5, female 0.5;
    * 1 to \< 2 years, male 0.6, female 0.6;
    * 2 to \< 6 years, male 0.8, female 0.8;
    * 6 to \< 10 years, male 1, female 1;
    * 10 to \< 13 years, male 1.2, female 1.2;
    * 13 to \< 16 years, male 1.5, female 1.4;
    * \>= 16 years, male 1.7, female 1.4.
* ENROLLMENT: Adequate liver function, defined as: total bilirubin =\< 2 mg/dl
* ENROLLMENT: Adequate liver function, as defined as serum glutamate pyruvate transaminase (SGPT) (alanine aminotransferase \[ALT\]) =\< 2.5 x upper limit of normal (ULN) for age (unless Gilbert's disease or abnormal liver function due to primary disease).
* ENROLLMENT: Evidence of adequate bone marrow function (defined by absolute neutrophil count \>= 750), unless patient has documented tumor metastasis to the bone marrow or other condition that results in cytopenia without abnormal marrow function.
* ENROLLMENT: Evidence of adequate bone marrow function (defined by platelets \>= 50,000), unless patient has documented tumor metastasis to the bone marrow or other condition that results in cytopenia without abnormal marrow function.
* ENROLLMENT: Pulmonary symptoms controlled by medication and pulse oximetry \>= 92% on room air.
* ENROLLMENT: Sexually active males and females of childbearing potential must agree to use a form of contraception considered effective and medically acceptable by the investigator. (Non-childbearing potential defined as pre-menarche, greater than one year post-menopausal or surgically sterilized).
* ENROLLMENT: Confirmation that a cord blood donor which is matched with the recipient at a 4, 5, or 6/6 human leukocyte antigen (HLA) class I (serological) and HLA class II (molecular) antigens.
* ENROLLMENT: Signed informed consent and if applicable pediatric assent.

Exclusion Criteria:

* SCREENING: Primary tumors of the central nervous system.
* SCREENING: Chronic corticosteroid dependence that is unable to be weaned to discontinue.
* SCREENING: Determined by study doctor that patient is unlikely to meet inclusion criteria after screening.
* ENROLLMENT: Uncontrolled arrhythmias or uncontrolled symptoms of cardiac disease noted by screening history and physical. Patients with known cardiac dysfunction should have an ejection fraction (EF) \> 40% documented by echocardiogram (ECHO).
* ENROLLMENT: Patients where the burden of pulmonary metastasis, location, or bulkiness of disease may cause high morbidity if localized swelling such as causing uncontrolled symptoms, oxygen dependence, or location near a major bronchi as determined by investigator.
* ENROLLMENT: Pregnant females.
* ENROLLMENT: Any uncontrolled systemic infection.