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A long-standing problem in the study of the under-hole-doped cuprates has been the description of the Fermi surfaces underlying the high magnetic field quantum oscillations, and their connection to the higher temperature pseudogap metal. Harrison and Sebastian [Phys. Rev. Lett.106, 226402 (2011)] proposed that the pseudogap “Fermi arcs” are reconstructed into an electron pocket by field-induced charge density wave order. But computations on such a model [Zhang and Mei,Europhys. Lett.114, 47008 (2016)] show an unobserved additional oscillation frequency from a Fermi surface arising from the backsides of the hole pockets completing the Fermi arcs. We describe a transition from a fractionalized Fermi liquid (FL*) model of the pseudogap metal, to a metal with bidirectional charge density wave order without fractionalization. We show that the confinement of the fermionic spinon excitations of the FL* across this transition can eliminate the unobserved oscillation frequency.