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We consider gamma-ray burst (GRB) jets that are choked by extended material as sources of high-energy cosmic neutrinos. We take into account the jet propagation physics both inside the progenitor star and the surrounding dense medium. Radiation constraints, which are relevant for high-energy neutrino production, are considered as well. Efficient shock acceleration of cosmic rays is possible for sufficiently low-power jets and/or jets buried in a dense, extended wind or outer envelope. Such conditions also favor GRB jets to become stalled, and the necessary conditions for stalling are explicitly derived. Such choked jets may explain transrelativistic supernovae (SNe) and low-luminosity (LL) GRBs, giving a unified picture of GRBs and GRB-SNe. Focusing on this unified scenario for GRBs, we calculate the resulting neutrino spectra from choked jets, including the relevant microphysical processes such as multipion production in pp and p-[gamma] interactions, as well as the energy losses of mesons and muons.