If someone gets destroyed by a Hakai, does he/she leave a ghost or is that obliterated alongside him/her?
I think this is already in its wikia page.
As Gods of Destruction, they possess the power to destroy almost anything with little effort, even intangible beings such as souls. People destroyed by Hakai do not go to Other World and simply cease to exist. However, in the manga, Beerus admits that Hakai does not work against people who are immortal.
Since the Other World is their equivalent to our afterlife where presumably, our ghost or spirit goes after death, then yes, Hakai can destroy someone including his/her ghost/spirit.
The technique however,
can be controlled by the user in moderation to not fully destroying the victim.
There are also a lot of variations of the said technique.