Why will j1311 (the black widow pulsar) eventually find itself without its companion star?

Because the pulsar is slowly destroying its companion.

Explanation:

J1311 is a fast spinning neutron star, which means it emits strong beams of radiation from it's poles.

As the beam of the pulsar sweeps across the surface of the companion star, it heats it up and blows its material outward into space, thus decreasing its mass.

As the pulsar continues sweeping its beam across the brown dwarf, it will continue to blow its material away, which eventually will evaporate the whole companion out of existence, thus leaving the pulsar without a companion star.

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This is straight from the course.