A mysterious X-ray-emitting object has been detected moving away from the high-mass gamma-ray binary PSR B1259-63, which contains a non-accreting pulsar and a Be star whose winds collide forming a complex interaction structure. Given the strong eccentricity of this binary, the interaction structure should be strongly anisotropic, which together with the complex evolution of the shocked winds, could explain the origin of the observed moving X-ray feature. We propose here that a fast outflow made of a pulsar-stellar wind mixture is always present moving away from the binary in the apastron direction, with the injection of stellar wind occurring at orbital phases close to periastron passage. This outflow periodically loaded with stellar wind would move with a high speed, and likely host non-thermal activity due to shocks, on scales similar to those of the observed moving X-ray object. Such an outflow is thus a very good candidate to explain this X-ray feature. This, if confirmed, would imply pulsar-to-stellar wind thrust ratios of $sim 0.1$, and the presence of a jet-like structure on the larger scales, up to its termination in the ISM.
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