We use the notion of double holography to study Hawking radiation emitted by the eternal BTZ black hole in equilibrium with a thermal bath, but in the form of warped CFT$_2$ degrees of freedom. In agreement with the literature, we find entanglement islands and a phase transition in the entanglement surface, but our results differ significantly from work in AdS/CFT in three major ways: (1) the late-time entropy decreases in time, (2) island degrees of freedom exist at all times, and not just at late times, with the phase transition changing whether or not these degrees of freedom include the black hole interior, and (3) the physics involves a field-theoretic IR divergence, emerging when the boundary interval is too big relative to the black holes inverse temperature. This behavior in the entropy appears to be consistent with the non-unitarity of holographic warped CFT$_2$ and demonstrates that the islands are not a phenomenon restricted to black hole information in unitary setups.
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