Which defunct countries still have valid passports

Another example: Hong Kong is no longer a British territory, but the British National (Overseas) passport is still valid despite its associated entity "British Hong Kong" being defunct.

https://en.wikipedia.org/wiki/British_National_(Overseas)_passport

The order of Malta does not control any territory any longer, (It is definitely not controlling Malta) but it still issues passport which are accepted by at least 110 countries and territorials

https://en.wikipedia.org/wiki/Sovereign_Military_Order_of_Malta_passport

Passports and ID cards of the German Democratic Republic, that were generally valid for 10 years, became invalid after the 31st of December 1995 (more than 60 months after the reunification).

At the end of January 1995, general announcements were made making people aware of this, so that a timely exchange could be made.

Personalausweise und Reisepässe der ehemaligen DDR verlieren Ende dieses Jahres ihre Gültigkeit. Das Potsdamer Innenministerium wies am Freitag darauf hin, daß die betroffenen Bürger möglichst bald bei den Einwohnermeldeämtern neue Dokumente beantragen sollten, um mögliche lange Wartezeiten gegen Jahresende zu vermeiden. Die Gebühren für einen neuen Personalausweis betragen 10, für den Euro-Paß 30 Mark.

Identity cards and passports of the former GDR are no longer valid at the end of this year. The Potsdam Ministry of the Interior announced on Friday that the citizens concerned should apply for new documents as soon as possible from the residents’ registration offices in order to avoid long waiting times towards the end of the year. The fees for a new ID card are 10 marks, for the Euro passport 30 marks.

An ID card issued in Berlin (West), which were different than those issued in West Germany, remained valid until they expired.

This scenario is definitely possible. For example, the Soviet Union broke up in 1991, but continued to issue passports until 1997, with 5-year validity extending to 2002, over 10 years later.

However, I’m not aware of any current cases where this is possible, because machine-readable passport validity is limited to ten years and (AFAIK) no country has become defunct in the last ten years. The last country to become independent was South Sudan in 2011, but Sudan did not cease to exist. There have also been some renamings like North Macedonia, with citizens using a mix of old and new passports, but the country itself is the same political entity.

In general, if a country accepts another country’s passport it is implicitly acknowledging the existence of that country. This is why sometimes the use of passports is a big issue in international relations.

The poster example would be the issues between the People’s Republic of China and the Republic of China (Taiwan). You may travel from one to the other, but you cannot use a passport of one to enter the other, because officially they do not recognize each other. A citizen of one of those countries will use instead a "travel permit" that works like a passport but is not called a passport so it does not imply official recognition.

So you could say that, as long a country A accepts your "defunct" country B’s passports, country B is not actually defunct (at least from country A’s POV).

Of course, if the desapparition of the country is recent and sudden, maybe you will have many citizens of that country that only have the "old" passport, and for a time it can be exceptionally accepted on practical grounds. And usually the new country that succeeds it will hurry up to issue its own documents (if needed, just by stamping some seals on the old passports) to make it the new situation clear.

I think it would go against the concept of a passport for it to be valid after the existence of the state itself. In its most basic sense, a passport is a request for someone to be granted passage through another state. See the Wikipedia article on passports. If the country ceases to exist, then its request for passage would as well.

For example, my Canadian passport reads:

The Minister of Foreign Affairs of Canada requests, in the name of Her Majesty the Queen, all those whom it may concern to allow the bearer to pass freely, without delay or hindrance, and to afford the bearer such assistance and protection as may be necessary.

Other countries have similar requests.

Now, could its passports still be accepted by some other countries? Perhaps. But I don’t think any would be "valid".