The goal of this clinical research study is to determine whether it is safe and practical to give CK0801 (a Cord blood-derived T-regulatory cell product) to patients with bone marrow failure syndrome. Researchers want to determine the highest possible dose that is safe to be given. Researchers also want to learn if CK0801 may improve the symptoms of bone marrow failure syndrome.

Patients enrolled in this study will all have been diagnosed with treatment refractory bone marrow failure syndrome (which includes aplastic anemia, myelodysplastic syndrome, or myelofibrosis). Participants eligible to participate in this study are unable or unwilling to be treated with standard therapy or have failed standard therapy.

Primary Objective:

To determine dose-limiting toxicity of CK0801 as defined as any of the events each start at the time of CK00801 infusion

1. Severe (grade 3 or 4) infusion toxicity within 24 hours (NCI-CTCAE V4.0)
2. Regimen related death within 30 days
3. Severe (grade 3 or 4) Cytokine Release Syndrome within 30 days

Secondary Objective:

1. Preliminary assessment of disease-specific response
2. Duration of disease-specific response

Inclusion Criteria:

1. Subjects who fulfill the diagnostic criteria of bone marrow failure syndrome including: aplastic anemia, myelodysplastic syndrome, or myelofibrosis.
2. HLA matched (≥ 3/6) cord blood unit available for CK0801 generation.
3. Subjects age ≥ 18 years.
4. Bilirubin ≤ 2 x ULN and SGPT (ALT) ≤ 2 x ULN (unless Gilbert's syndrome is documented).
5. Calculated creatinine clearance of > 50mL/min using the Cockcroft-Gault equation.
6. Zubrod performance status ≤ 2.
7. Female subjects of child bearing potential (FPCP) must have a negative urine or serum pregnancy test. NOTE: FPCP is defined as premenopausal and not surgically sterilized. FPCP must agree to use maximally effective birth control or to abstain from heterosexual activity throughout the study. Effective contraceptive methods include intra-uterine device, oral and/or injectable hormonal; contraception, or 2 adequate barrier methods (e.g., cervical cap with spermicide, diaphragm with spermicide).
8. Subject has agreed to abide by all protocol required procedures including study-related assessments, visits and long term follow up.
9. Subject is willing and able to provide written informed consent.

Exclusion Criteria:

1. Subject has received an investigational agent within 4 weeks prior to CK0801 infusion.
2. Subject has received radiation or chemotherapy within 21 days prior to CK0801 infusion.
3. Subject has received prior cord blood-derived T-regulatory therapy.
4. HIV seropositivity.
5. Subject has uncontrolled infection, not responding to appropriate antimicrobial agents after seven days of therapy. The Protocol PI is the final arbiter of eligibility.
6. Subjects with uncontrolled inter-current illness that in the opinion of the investigator would place the patient at greater risk of severe toxicity and/or impair the activity of CK0801
7. Subjects is pregnant or breastfeeding.
8. Bone marrow failure caused by stem cell transplantation.
9. Subjects who are unable to provide consent or who, in the opinion of the Investigator will be unlikely to fully comply with protocol requirements.