US copyright law has been continually updated since the 1970's, with a primary aim of keeping Mickey Mouse from entering the public domain. As a result, not many works since the mid-1920's have entered the public domain. The current length of a copyright is the life of the creator plus 70 years. Before 1978 the copyright period was 28 years, which could be extended another 28. Imagine that someone made a recording in 1949. It would have come up for copyright renewal in 1977. If they renewed it, then the copyright would have still been in force when it crossed the magic date of 1978, getting an extension to life plus 50 (at that time). But if the copyright holder did not renew the item in 1977, then it entered the public domain that year, and copyright would not re-attach in 1978 when the law was changed.
The creator can sign away all rights to a work, in which case the copyright period is still tied to that person's life, but all royalties go to whoever bought it. This most often happened in publishing, such as some magazine publishing, but may have occurred in music, for all I know. Tracing the provenance of copyright to a work can be a daunting task; I recall reading a brief the length of a novella tracing the copyrights of H. P. Lovecraft's fiction, coming in the end to the conclusion that it had all entered the public domain.
Once a work enters the public domain, it means that anyone can re-release it and make money off it. This is why you can easily get a collected works of Sherlock Holmes, but not of Kurt Vonnegut: anyone can publish the Holmes stories (and anyone can make a movie about the character, which also entered the public domain long ago), and if they sell their copies, they keep the money. Vonnegut's stuff is still under copyright. If you want to reprint it, you have to get permission from Vonnegut's heirs and pay royalties.
Assuming the rights still belonged to the musician at the time of death, the royalties go to the estate and are handled according to the artist's will. They are divided among the heirs in the will. If the heirs die, then their royalties are distributed according to the terms of their wills, unless the creator's will limited the transfer to the person named and not their heirs or assignees. If the artist had no will, then the artist's royalties are divided up according to the State's rules regarding those who die intestate. So a great deal depends on when the work was created, when the person died, and where they lived (the state whose laws will govern the execution of a will). To my knowledge, there is no state that simply keeps the money. Record companies may very well try to do so, but they'll be in deep trouble at their first audit. Law, after all, was originally created to protect property, not people, and protection of property is still one of its main functions.
In the final analysis, you're probably best off deciding to retract your question and leave it all up to the attorneys.