At the moment, PopIII stars are still hypothetical.
From the paper about the "impossible" star (SDSS J102915+172927):
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Stars similar to SDSS J102915+172927 are probably not so rare. Only 30% of the whole SDSS survey area was accessible to our VLT observations. We identified 2899 potentially extreme stars with metallicity less than Z ≤1.1×10*^5 in Data Release 725. Among those observable with the VLT we performed a subjective selection of the most promising candidates of which we observed six in our X*Shooter programme resulting in one detection. Depending on the subjective bias we attribute to the last selection step, we expect 5 to 50 stars of similar or even lower metallicity than SDSS J102915+172927 to be found among the candidates accessible from the VLT, and many more in the whole SDSS sample.
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So, based on the current data, it looks like these PopII stars might be quite common, but the lower the metallicity, the fewer they are in number.
Lithium depletion seems to be a characteristic shared with blue stragglers and suggests that the stellar material has experienced temperatures about 2 million Kelvin. The origins may be the same, or they may share the same unusual formation conditions, in terms of the mixture of elements from the start.
Cheers