Peginterferon Alfa-2b in Younger Patients With Craniopharyngioma That is Recurrent or Cannot Be Removed By Surgery

Inclusion Criteria: * Patient must have a histologically verified diagnosis of craniopharyngioma * Stratum 1: patients with progressive unresectable or recurrent craniopharyngiomas treated with surgery alone, who have not received radiation therapy; patients with unresectable craniopharyngiomas, (i.e. residual measurable disease following surgical resection) will be enrolled at the time of progression * Stratum 2: patients with progressive or recurrent craniopharyngiomas following radiation therapy * All patients must have measurable residual disease defined as tumor measurable in two perpendicular diameters on magnetic resonance imaging (MRI) * Please note: measurements are required for both the solid and cystic components * Subjects must have recovered from the acute toxicities of all prior therapy before entering this study; for those acute baseline adverse events attributable to prior therapy, recovery is defined as a toxicity grade =\< 2, using Common Terminology Criterial for Adverse Events (CTCAE) version (v.) 4.0, unless otherwise specified in the inclusion and exclusion criteria * Myelosuppressive chemotherapy (includes intra-cystic bleomycin): * Subjects must have received their last dose of known myelosuppressive anticancer chemotherapy at least three (3) weeks prior to study registration or at least six (6) weeks if nitrosourea * Subjects must have received their last dose of investigational or biologic agent \>= 7 days prior to study registration * In the event that a subject has received an investigational or biologic agent and has experienced \>= grade 2 myelosuppression, then at least three (3) weeks must have elapsed prior to registration * If the investigational or biologic agent has a prolonged half-life (\>= 7 days) then at least three (3) weeks must have elapsed prior to registration * Subjects must have completed at least 3 half-life periods from the last dose of monoclonal antibody prior to registration * Note: a list of half-lives of commonly used monoclonal antibodies is available on the Pediatric Brain Tumor Consortium (PBTC) website under Generic Forms and Templates * Stratum 1: patients must not have received radiation therapy * Stratum 2: patients must have received radiation therapy, including gamma knife or phosphorus-32 (P32) * More than 6 months from the time of enrollment if the recurrence is predominantly solid * More than 12 months from the time of enrollment if the recurrence is predominantly cystic * At least 7 days since the completion of therapy with a hematopoietic growth agent (filgrastim, sargramostim, and erythropoietin) and 14 days for long-acting formulations * Karnofsky performance scale (KPS for \> 16 years \[yrs\] of age) or Lansky performance score (LPS for =\< 16 years of age) \>= 60 assessed within two weeks prior to registration * Age: 18 months - 25 years (Minimum weight 20 Kilogram is required to be eligible for the study, since the minimum injection volume of SYLATRON is 0.05 ml, 20 mcg, subcutaneously (SQ) as suggested by Merck) * Absolute neutrophil count (ANC) \>= 1000/ul (unsupported) * Platelets \>= 100,000/ul (unsupported) * Hemoglobin (Hg) \>= 8g/dL (unsupported) * Alanine aminotransferase (ALT) =\< 2.5 x the upper limit of institutional normal * Total bilirubin =\< x 1.5 upper limit of institutional normal * Serum creatinine =\< 1.5 x the upper limit of normal for age, or calculated creatinine clearance or nuclear glomerular filtration rate (GFR) \>= 70 ml/min/1.73 m\^2 * =\< 0.6 mg/dL (1 to \< 2 years of age) * =\< 0.8 mg/dL (2 to \< 6 years of age) * =\< 1.0 mg/dL (6 to \< 10 years of age) * =\< 1.2 mg/dL (10 to \< 13 years of age) * =\< 1.4 mg/dL (females \>= 13 years of age) * =\< 1.5 mg/dL (males 13 to \< 16 years of age) * =\< 1.7 mg/dL (males \>= 16 years of age) * All patients must have undergone at least one surgical procedure to verify the diagnosis * Patients must have evidence of radiographic progression as defined below: * Stratum 1: defined as \>= 25% increase in the product of the greatest perpendicular diameters of the tumor as a whole (solid and cystic component) AND \>= 0.4 cm increase in each of at least two dimensions of the tumor as a whole OR any new or worsening neurologic/vision deficit in conjunction with a lesser change in the solid or cystic component * Stratum 2: * For patients more than 6 months following radiation therapy (RT) (including radiosurgery or P32), progression is defined as a \>= 25% increase in the product of the greatest perpendicular diameters of the solid component AND \>= 0.4 cm increase in each of at least two dimensions of the solid component * For patients more than 12 months following RT (including radiosurgery or P32), progression is defined as \>= 25% increase in each of the product of the greatest perpendicular diameters of the solid tumor AND \>= 0.4 cm increase in each of at least two dimensions of the solid tumor; patients demonstrating isolated cyst progression more than 12 months after RT must show a continued increase in the cystic component on two serial MRI scans performed at least 4 weeks apart OR re-accumulation of the cyst following one or more cyst aspirations; patients with progressive neurologic signs and/or symptoms associated with isolated cyst formation or progression are eligible if the neurologic signs and/or symptoms do not improve within 4 weeks of cyst aspiration * Female subjects of childbearing potential must not be pregnant or breast-feeding; female subjects of childbearing potential must have a negative serum or urine pregnancy test; (pregnancy test must be repeated within 72 hours prior to the start of therapy) * Subjects of childbearing or child fathering potential must be willing to use a medically acceptable form of birth control, which includes abstinence, while being treated on this study * Ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * Stratum 1 patients: must not have had \> 3 surgical debulking procedures/resections * Patients may not have received prior interferon, either systemic or intra-cystic * Patients must not have evidence of metastatic tumor * Patients must not be on steroids other than for physiologic replacement * Patients must not have a severe psychiatric illness, including major depression or any previous suicide attempts * Patients must not be on phenytoin, warfarin or methadone due to potential drug interactions * Patients must not have known hypersensitivity reactions, such as urticaria, angioedema, bronchoconstriction, anaphylaxis, Steven-Johnson syndrome, and toxic epidermal necrolysis to interferon alpha or any other products component * Subjects with inability to return for follow-up visits or obtain follow-up studies required to assess toxicity to therapy