Souls that cross over the Sanzu River will arrive in Higan to await their judgement. Depending on the Yama's verdict, they may indeed be reincarnated.
It is implied that a soul can be taken out of the reincarnation cycle entirely by certain means, such as when Kasen uses her right arm to crush a vengeful spirit, but I don't believe it's explained whether this works on any type of soul, as even Komachi was a bit confused at what exactly had happened.
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