Budhism that does not have hell and heaven does not also accept soul. It is karma that moves around.
Advaita Hinduism does not have hell and heaven because it believes in a universal substrate, Brahman, to constitute each and everything in the universe.
So, in this case, things/beings arise out of the substrate, Brahman, dissipate again into the substrate.
"Avināśi tu tad viddhi, yena sarvam idaḿ tatam;
vināśam avyayasyāsya, na kaścit kartum arhati"
That which pervades all this you should know to be indestructible. No one is able to destroy that imperishable. BhagawadGita 2.17