Vela X is a pulsar wind nebula (PWN) associated with the active pulsar B0833-45 and contained within the Vela supernova remnant (SNR). A collimated X-ray filament ("cocoon") extends south-southwest from the pulsar to the center of Vela X. VLA observations uncovered radio emission coincident with the eastern edge of the cocoon, and H.E.S.S. has detected TeV 7-ray emission from this region as well. Using XMM-Newton archival data, covering the southern portion of this feature, we analyze the X-ray properties of the cocoon. The X-ray data are best fit by an absorbed nonequilibrium plasma model with a power-law component. Our analysis of the thermal emission shows enhanced abundances of O, Ne, and Mg within the cocoon, indicating the presence of ejecta-rich material from the propagation of the SNR reverse shock, consistent with Vela X being a disrupted PWN. We investigate the physical processes that excite the electrons in the PWN to emit in the radio, X-ray, and 7-ray bands. The radio and nonthermal X-ray emission can be explained by synchrotron emission. We model the 7-ray emission by inverse Compton scattering of electrons off of cosmic microwave background (CMB) photons. We use a three-component broken power law to model the synchrotron emission, finding an intrinsic break in the electron spectrum at ～5 × 10~6 eV and a cooling break at ～5.5 × 10~(10) keV. This cooling break along with a magnetic field strength of 5 × 10~6 G indicate that the synchrotron break occurs at ～1 keV.
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