  Mounting evidence suggests that the launching of collapsar jets is
magnetically driven. Recent general relativistic magneto-hydrodynamic
simulations of collapsars reveal that the jet is continuously loaded with
baryons, owing to strong mixing with the cocoon. This results in a high
photosphere at $\gtrsim 10^{12}$ cm. Consequently, collisionless internal
shocks below the photosphere are disfavored, and the neutrino production in the
deepest jet regions is prevented, in contrast to what has been assumed in the
literature. We find that subphotospheric neutrino production could only take
place in the presence of collisionless sub-shocks or magnetic reconnection.
Efficient particle acceleration is not possible in the cocoon, at the
cocoon-counter cocoon shock interface, or at the shock driven by the cocoon in
the event of a jet halted in an extended envelope. These subphotospheric
neutrinos have energy $E_\nu \lesssim 10^5$ GeV for initial jet magnetizations
$\sigma_0=15$-$2000$. More than one neutrino and antineutrino event is expected
to be observed in Hyper-Kamiokande and IceCube DeepCore for sources located at
$z \lesssim \mathcal{O}(0.1)$. Because of their energy, these neutrinos do not
contribute to the diffuse flux detected by the IceCube Neutrino Observatory.
Our findings have implications on neutrino searches ranging from gamma-ray
bursts to luminous fast blue optical transients.
