Fludarabine Phosphate, Cyclophosphamide, Total Body Irradiation, and Donor Stem Cell Transplant in Treating Patients With Blood Cancer

Inclusion Criteria: * Any disease that is considered transplant eligible per TCT standards * Disease response noted (i.e. CR, non-CR, or not applicable): Assessed as per disease specific criteria * Suitable related haploidentical donor identified per transplant service: * Recipient should not have HLA antibodies to potential donor. If the recipient does have HLA antibodies to the potential donor, an alternative donor is preferred; however, if there are no suitable alternative donors, the anti-HLAt antibodies should be depleted per transplant service guidelines. * Haploidentical donors that are ABO compatible with the recipient are preferred. Minor ABO incompatibility is preferred to major ABO incompatibility. Major ABO incompatibility between recipient and donor is the least preferred but still acceptable for this study. * It is preferred that the haploidentical donor must be available to donate on day -1 and day 0, so that fresh product can be processed by the Stem Cell lab and administered to the patient on day 0.While less preferable, cryopreserved product may be utilized with this product. * Diffusing capacity of the lung for carbon monoxide (DLCO) \> 40% predicted, corrected for hemoglobin and/or alveolar ventilation * Left ventricular ejection fraction \> 40% * Bilirubin, liver alkaline phosphatase, serum glutamic-oxaloacetic transaminase (SGOT) or serum glutamate pyruvate transaminase (SGPT) =\< 3 x upper limit of normal * Calculated creatinine clearance \> 40 cc/min by the modified Cockcroft-Gault formula for adults or the Schwartz formula for pediatrics * Have a Karnofsky (adult) or Lansky (for =\< 16 years) performance status \>= 60% * Patient must be able to pass radiation evaluation (i.e.: able to receive 200 cGy) * Patients who have failed a prior autologous transplant are eligible; however, at least 90 days must have elapsed between the start of this reduced intensity conditioning regimen and the last transplant if patient had a prior autologous BMT * Participants of child-bearing potential must agree to use adequate contraceptive methods (e.g., hormonal or barrier method of birth control; abstinence) prior to study entry; should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately * Participant must understand the investigational nature of this study and sign an independent ethics committee/Institutional Review Board approved written informed consent form prior to receiving any study related procedure * If patient is planned to use a fully matched donor, patient is excluded from trial; patient must be planned to undergo a haploidentical matched transplant to participate on study. Patient is still eligible for trial regardless of donor options if PI feels that haplo transplant is in the patient's best interest per clinical decision * Exclusion Criteria: * Participants who have had chemotherapy (not including molecularly targeted agents; examples include, but are not limited to, tyrosine kinase inhibitors such as FLT3 inhibitors and IDH2 inhibitors), radiation treatment and/or surgery 7 days prior to starting conditioning regimen. Those who have not recovered sufficiently from adverse events due to agents administered more than 2 weeks earlier are also ineligible. Exceptions may be made on a case-by-case basis after discussion with the PI * Uncontrolled central nervous system (CNS) disease (for hematologic malignancies) Per PI discretion * Child-Pugh class B and C liver failure * Concomitant active malignancy that would be expected to require chemotherapy within 3 years of transplant (other than non-melanoma skin cancer) Exception would include any concurrently existing malignancy that could be treated with a transplant per PI discretion (Example: Patient has AML but a history of mastocytosis) * Patients who have received maximally allowed doses (given in 2 Gy fractionations, or equivalent) of previous radiation therapy to various organs; patients who previously have received a higher than allowed dose of radiation to a small lung, liver and brain volume, will be evaluated by the radiation oncologist to determine if the patient is eligible for study * Uncontrolled diabetes mellitus, cardiovascular disease, active serious infection or other condition which, in the opinion of treating physician, would make this protocol unreasonably hazardous for the patient * Known human immunodeficiency virus (HIV) positive * Pregnant or nursing female participants * Patients who in the opinion of the treating physician are unlikely to comply with the restrictions of allogeneic stem cell transplantation based on formal psychosocial screening * Patients with donor specific HLA antibodies with a titer greater than 3000 MFI (whether or not they have undergone a desensitization protocol) * Patients who have undergone a prior allogeneic hematopoietic or (other organ) transplant * Treating physician considers the potential HLA haploidentical donor to be ineligible to receive G-CSF, and/or concern on the part of the treating physician for risk of harm to the potential donor with administration of G-CSF, and/or refusal by the potential donor (or donor's guardian) to receive G-CSF * Any condition which in the investigator's opinion deems the participant an unsuitable candidate to receive study drug * Received an investigational agent within 14 days prior to enrollment. Exceptions may be made on a case-by-case basis after discussion with PI