There is reform under discussion to grant PR and/or citizenship to a majority of them - https://thailand.un.org/en/285279-unhcr-supports-thailand-ma...
Entire families live and die stateless. Alien travel documents exist in some circumstances (as referenced by this guide) but are a very obscure thing, hard to obtain and the process may be arbitrary, airline staff and border immigration officers are frequently not familiar with them, etc.
This is usually not a status that anyone holds voluntarily; they are displaced at some point and the government which controls the territory they are displaced into does not want to enfranchise them, or even their descendants.
All told globally there are 4-5 million stateless people.
From an interview with the author: https://www.weforum.org/stories/2022/09/young-global-leaders...
Practically, there is no point for the state to deny you citizenship if you went to school there and can do some kind of a job and pay taxes, because they can't even deport you to a country of origin if you are stateless and born there.
Technically even the US has the jurisdiction qualifier, which the orange clown wants to abuse.
[1]: https://taejun.substack.com/p/founders-peak-speech-script
I do find it quite unusual that he would not be allowed to naturalize after living all his life here and being married to a Japanese citizen, so perhaps there are other exceptional circumstances. Or perhaps his statelessness isn't something he is actively trying to resolve, having found ways to work around it when he needs to travel and do other things.
I know someone who tried to start the naturalization process but was instantly shot down for his Japanese skill (he speaks Japanese well). I know others who have lived in Japan for decades but cannot apply for permanent residency because they only receive short visas, making them ineligible.
Immigration officers have ultimate discretion and will not explain themselves to applicants. I assume this is by design so that particular 'standards' can be subtly applied without being reflected in statistics or receiving any criticism.
Unrestricted jus soli (extending nationality unconditionally to those born in the territory of the state, regardless of ancestry) is largely an American (as in "of the Americas", not merely "of the United States of America", though the latter is a significant reason why it is true of the former) thing, though there are a few countries outside of the Americas who do it as well.
Some more countries have restricted jus soli, extended to those born in the territory of the state only if the government judges them to be ineligible for nationality by the law of any other state, or perhaps only if the parents are actually stateless, as a way to mitigate statelessness. (And states who have adopted a rule of this type for this purpose may have done so after the UN Convention on stateless persons in 1954, and may not have applied it retroactively.)
[1] https://bosniaherzegovina.un.org/en/234262-live-without-nati...
But the US is, of course, a fairly unique case here. Most people become stateless due to state persecution (famously many Jews were stripped of their German citizenship by the 1935 Nuremberg laws, and many Kurds were denied Syrian citizenship under Assad) or by falling through weird administrative cracks (for example, see the cases of Mehran Karimi Nasseri [3] and Shamima Begum [4]). There are also cases (e.g. many Druze in Israel and the occupied Golan Heights) who refuse to accept citizenship they are offered on political grounds,[5] who would be considered de facto stateless if they do not have another recognised citizenship (though I'm not sure how Israeli citizenship works; the US considers you a citizen with worldwide tax obligations whether you accept it or not).
The interim solution is to get a 1954 Convention Travel Document[6] from one of the signatory states, which functions like a passport (and taxes in most countries are levied based on residence, rather than citizenship, so you'll still be paying them already). For a permanent solution, you'd need to go through the normal naturalisation process to become a citizen of a new country.
[0] https://en.wikipedia.org/wiki/Statelessness#United_States
[1] https://www.vice.com/en/article/a-bum-without-a-country-0000...
[2] https://dollarvigilante.com/2015/07/20/interview-with-glen-r...
[3] https://en.wikipedia.org/wiki/Mehran_Karimi_Nasseri#Life_in_...
[4] https://en.wikipedia.org/wiki/Shamima_Begum#Citizenship
[5] https://en.wikipedia.org/wiki/Druze_in_Israel#Status_of_Druz...
I'm not entirely sure how that works out and which citizenship someone living in Gaza or the Westbank would fall under. In any case I can't imagine that a Palestinian passport holds much value.
As a result the parents can get citizenship, but don't want to, as authorities don't bother them much, but their now adult child is technically a citizen, but doesn't have paperwork to prove their status.
If you actually bothered for 3 seconds with checking actual article, its very first line