We carry out a detailed study of the confinement phase transition in a dark sector with a $SU(N)$ gauge group and a single generation of dark heavy quark. We focus on heavy enough quarks such that their abundance freezes out before the phase transition and the phase transition is of first-order. We find that during this phase transition the quarks are trapped inside contracting pockets of the deconfined phase and are compressed enough to interact at a significant rate, giving rise to a second stage of annihilation that can dramatically change the resulting dark matter abundance. As a result, the dark matter can be heavier than the often-quoted unitarity bound of $sim100~$TeV. Our findings are almost completely independent of the details of the portal between the dark sector and the Standard Model. We comment briefly on possible signals of such a sector. Our main findings are summarized in a companion letter, while here we provide further details on different parts of the calculation.
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