[Efendija]

It can be awfully complicated. Companies usually secure the rights for a certain time period. A lot of the specifics can be worked out through a contract though. Various things come into play, e.g. author can be a regular employee of the company or a freelance who gets hired for a specific work etc.

Rights can't last forever and all works will eventually enter the public domain. PD for game music isn't of use to any of us because we'll be long gone when it happens. For example the US law:

Spoiler:

Works Created on or after January 1, 1978
The law automatically protects a work that is created and fixed in a tangible medium of expression on or after January 1, 1978, from the moment of its creation and gives it a term lasting for the author's life plus an additional 70 years. For a "joint work prepared by two or more authors who did not work for hire," the term lasts for 70 years after the last surviving author's death. For works made for hire and anonymous and pseudonymous works, the duration of copyright is 95 years from first publication or 120 years from creation, whichever is shorter

But before entering the PD, assuming the author had the relevant rights at the time of death and not compan(ies) which may still hold some of them, the successors get them.

In any case, you asking the right person/company to release the OSTs will hardly make a difference.