  We investigate the angular momentum removal from fission fragments (FFs)
through neutron and $\gamma$-ray emission, where we find that about half the
neutrons are emitted with angular momenta $\ge 1.5\hbar$ and that the change in
angular momentum after the emission of neutrons and statistical $\gamma$ rays
is significant, contradicting usual assumptions. Per fission event, in our
simulations, the neutron and statistical $\gamma$-ray emissions change the spin
of the fragment by 3.5 -- 5~$\hbar$, with a large standard deviation comparable
to the average value. Such wide angular momentum removal distributions can hide
any underlying correlations in the fission fragment initial spin values. Within
our model, we reproduce data on spin measurements from discrete transitions
after neutron emissions, especially in the case of light FFs. The agreement
further improves for the heavy fragments if one removes from the analysis the
events that would produce isomeric states. Finally, we show that while in our
model the initial FF spins do not follow a saw-tooth like behavior observed in
recent measurements, the average FF spin computed after neutron and statistical
$\gamma$ emissions exhibits a shape that resembles a saw tooth. This suggests
that the average FF spin measured after statistical emissions is not
necessarily connected with the scission mechanism as previously implied.
