Eltrombopag Olamine in Treating Thrombocytopenia in Patients With Chronic Myeloid Leukemia or Myelofibrosis Receiving Tyrosine Kinase Therapy

Inclusion Criteria:

* CML patients in chronic phase receiving treatment with any Food and Drug Administration (FDA) approved TKI; or CML patients in accelerated or blastic phase who are considered to be in this phase because of thrombocytopenia or because of clonal evolution and with no other criteria for accelerated/blastic phase or patients with myelofibrosis receiving treatment with FDA approved TKI and with peripheral blood and/or bone marrow blasts =\< 10%
* Grade \>= 3 thrombocytopenia (platelets \< 50 x 10\^9/L) after the first 3 months of therapy with the TKI for patients with CML and platelets \< 100 x 10\^9/L for patients with MF after the first 3 months of therapy; thrombocytopenia must be either recurrent (i.e., second or greater episode of thrombocytopenia) or having required dose reductions of the TKI
* Subject is anticipated to have therapy with TKI continued for \>= 3 months
* Total bilirubin =\< 1.5 x upper limit of normal (ULN) (except for Gilbert's syndrome)
* Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) \< 3 x ULN
* Creatinine =\< 2 x ULN

Exclusion Criteria:

* CML patients in accelerated or blastic phase except for those who are considered to be in this phase because of thrombocytopenia or because of clonal evolution and with no other criteria for accelerated/blastic phase; or myelofibrosis patients who have transformed to acute leukemia or have \>= 10% blasts in peripheral blood and/or in bone marrow
* Thrombocytopenia that is considered to be unrelated to treatment with TKI or accelerated phase as defined above
* Stem cell transplantation within preceding 60 days prior to registration
* Patients with documented active hepatitis B or C infection
* Patients with known bone marrow reticulin fibrosis (\>= grade 2) (only applicable to patients with CML)
* Patients with palpable splenomegaly \>= 16 cm below coastal margin (only applicable to patients with CML)
* Female subjects who are pregnant or breastfeeding
* Women of childbearing potential are required to have a beta human chorionic gonadotropin (BHCG) serum or urine pregnancy test performed within 7 days prior to first study drug dose; a female of childbearing potential is a sexually mature woman who:

  * Has not undergone a hysterectomy or bilateral oophorectomy
  * Has not been naturally postmenopausal for at least 12 consecutive months (i.e., has had menses at any time in the preceding 12 consecutive months)
* Women of child-bearing potential and men must agree to use contraception prior to study entry and for the duration of study participation
* Patients with known risk factors for thromboembolism (e.g. Factor V Leiden mutation, antithrombin III (ATIII) deficiency, Protein C and S deficiency, antiphospholipid syndrome, portal hypertension, etc.)