The precipitated chromatin now is supposedly only those fragments of DNA that are crosslinked with KLF1 and bound to Anti-KLF1 antibodies.
After precipitation, elution is necessary to interrupt the interaction between the antibodies and the chromatin (Antigen-Antibody interaction). This can be achieved by adding elution buffer that will lead to disruption of the pH and hence breaking the Ag-Ab interaction
The result will be two different products: an antibody by itself and an antigen, KLF1-bound to DNA.