Over a decade of work has culminated in the consensus that one-dimensional systems, subject to sufficiently large disorder, fail to thermalize and possess an extensive set of local integrals of motion. In this Letter, I will provide numerical evidence for the contrary. In particular, this work studies the dynamics of disordered spin chains which are weakly coupled to a Markovian bath. Within this approach, the critical disorder for stability to quantum avalanches exceeds $W^{*}\gtrsim 20$ in the random field Heisenberg chain. In stark contrast to the Anderson insulator, the avalanche threshold drifts considerably with system size, with no evidence of saturation in the studied regime.

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• Many-body localization
• Markovian processes
• Spin chains