What happens to the contents of the vault when everyone dies

Depending from artist to artist it's more likely that unreleased things get released after too many members die.
Look what came out after Michael Jackson's death. His last album came out in 2001 and from what I've heard he didn't liked his own stuff later.

I gave up thinking that any more good content will be ever released by Queen productions.
Too many let downs over the years.

I would have thought their children would inherit the status.

the members own the intellectual property through their corporations. the members or the members' trusts own shares of the corporation. usually voting rights are with living members and families share in the growth (income splitting and such). eventually when the voting members die, their will dictates how their assets - such as the shares with voting rights - are allocated. could be wives, children, friends, etc. eventually those that have the voting rights can do as they wish.

If they did not take part in the business while the members were living - usually someone that managed that business would step up and give some advice. usually this leads to them hiring legal help which will lead to a bunch of lawyers communicating together to ideally get the right people together to manage the assets of the band. lots of disputes occur when at least one member is still living - ie. The Doors, The Beatles, Nirvana - lots of articles out there.

However, when they're all dead - the advice is to exploit the vault to make the most money possible before their legacy is forgotten and void of value. Best time is as soon as possible after death. Think David Bowie and Prince - although not bands, this is probably the theory behind why there are so many releases.

My guess is Brian is the protective one. So as grim as it may sound - once Brian goes, regardless of who inherits his "shares", the catalog will likely be exploited.

I can see their wills now.... "Nothing unreleased is to ever be released!"