If a country was confident they developed a technology that would act as a fool proof deterrent against nuclear attacks what would that mean for the rest of the world?

US and Russia used to have a treaty against either country developing anti-ballistic missiles. The idea was that if 1 party trusted their ABMs too much, they would no longer care about a counter attack, and that would undermine the MAD doctrine.
https://en.m.wikipedia.org/wiki/Anti-Ballistic_Missile_Treaty
- So... you're talking about playing by the rules I'm talking about something different.
  
  They're talking about a treaty designed to prevent the result of the exact situation you're asking about. Extrapolating a step gives you at least one answer to your question.

Turns out, having a bunch of nukes is a pretty foolproof deterrent
- OP's learning what we kids knew in the 80s.
  War is just another game,
  Tailor made for the insane,
  But make a threat of their annihilation,
  And nobody wants to play,
  If that's the only thing that keeps the peace,
  [Chorus] Then thank God for the bomb!
- I mean… for now. How long until drones with thrusters on their backs can land on a missle and redirect it wherever they want?
  
  Give Ukraine 6months they'll figure it out

They already have - having Nukes.
- They already have - having Nukes.
  That only defends against a sane leadership with a military chain of command that isn't compromised.
  
  Seems to have gone pretty well for the last 80 years or so. Don’t see any reason why that would change.
- sigh
  Nm
  
  Also, if you meant that a country created some sort of perfect defence against nukes, then every other country would immediately start pouring money into creating their own version, while working on ways of subverting the new technology.

I think the US has already achieved it and aren’t saying anything.
Think how much money they’ve poured in there over the decades, as much as the rest of the world combined.
They were working on directed energy weapons in the 80s to neutralise them from space, but the tech was ‘decades away’. They had a working pilot way back in 2000 too.
- They definitely have not. Not publicizing a fool proof nuclear counter-measure defeats the purpose of achieving it in the first place.
  You'd MUCH rather your opponent know a nuke strike is pointless, rather than they try and later be surprised that only one lucky one got through.
  
  Arguably, you don't tell them, and they don't try to steal the idea, or try to sabotage it, or decide to build was plans that don't depends on a successful nuclear strike.
  
  One of the biggest challenges when creating something new is in not knowing whether or not it's possible. Once you know, you can just keep pouring resources into it and know with near certainty that you'll eventually hit your goal. Since the US already has so many other tools for avoiding a nuclear strike, there's no reason to publicise a new one. Keep it for when the other tools fail, or else everyone else will also have it and you lose your advantage before you could use it.
  
  It depends on the reliability.
  If you announce it, there are often counter measures to the counter measures. Once the enemy knows, the reliability begins to degrade. E.g. mirror finishes can disperse laser strikes, jinking can doge orbital rail guns, or dummy submunitions can overwhelm interceptor shields. Yes, these can be countered in turn, but you now have a new technological arms race.
  There's also the first strike problem. If you are going to be invulnerable, then a first strike might be reasonable, before the system comes online. This was actually part of the reason the "Slam" project was stopped (a viable, but utterly batshit insane weapon system). They were worried that if the USSR got wind of it, they might decide a first strike, before it came online, was the only reasonable response.
  
  Not publicizing a fool proof nuclear counter-measure defeats the purpose of achieving it in the first place.
  yeah but if they don't tell anyone they can keep it secret and other countries wouldn't try to make their own
  
  Not if the technology is relatively unknown. I mean, maybe if you were alturistic.
  
  If made public there’d be attempts to sabotage the system that they’re avoiding.
- Ok, how do you feel about elon musk (and subsequently russia) gaining access to some of our most classified data.
  
  We’re cooked.

How does confidence factor into this? I've been confident in stuff before and it turned out that confidence was misplaced. Pride cometh before the fall shit. Confidence alone risks cockiness. Cockiness may lead to somebody testing your Golden Shield. Didn't work. You now don't have a country any more.
If the Golden Shield really worked it's a question of capacity. If you had enough juice in it to repel all nuclear weapons you could throw at this country in a worst-case scenario, you'd have a powerful defense against the most powerful weapon on Earth that's ready to deploy this minute. It may not save you from conventional attacks. It may not shield you from chemical or biological weapons so gruesome they aren't currently shelf-ready. But development of those would suddenly become a viable prospect. I fear it just turns the spiral of development of more destructive weaponry one more rotation. Extrapolating from the last 6000 years of history, we've gone from sticks and stones to vaporizing people into thin mist by harnessing the power of the atom. We're already in the narrow bit of the spiral. Paradoxically, developing a Golden Shield against nuclear attacks may lead to wiping our species out for good.

We already have it, they're called nuclear bombs, and MAD.
- How is that fool proof?
  
  “The nuclear arms race is like two sworn enemies standing waist deep in gasoline, one with three matches, the other with five.”
  ― Carl Sagan
  
  It is proof that humans are fools
  
  Hasn't failed yet (yes I know that's the survivorship bias fallacy)
  
  This points to a flaw in your question.
  You probably should have said “foolproof countermeasure” if you really just wanted to remove nukes as a factor to see what happens.
  But you said “foolproof deterrent” and now you’re quibbling at people over whether a psychological deterrent can actually be foolproof.
  Maybe not, but then your question is nonsensical. The fact is that we are already using guaranteed total destruction of the world as a deterrent and it has so far worked. What more deterrence are you even suggesting we might add to that???

Probably more war:
Depending on the country who developed it, the risk of nuclear war could go up.
If I don't have to worry about nuclear retaliation, maybe I'm very confident in engaging in war. After all, my nukes will still work, and everyone else's won't.
If the technology is shared equally to all countries at the same time, the risk of conventional war could go up.
Imagine the nuclear armed countries who are enemies of another nation with a bigger military. North Korea vs USA, Pakistan vs India. In these cases, nuclear weapons are a deterrence against the stronger opponent. Without this, the country with a stronger conventional force may be more likely to they think they'll win a war unscathed.

It would depend on the tech.
Low tech: e.g. detect and destroy incoming weapons....if a single major power had this, it would bad. They maybe emboldened to use their weapons (both nuke and conventional), as their perfect defense would keep their assets (people, places, weapon systems) safe.
High tech: e.g. directed EMP type weapon that could eliminate any weapon world wide at launch, this would eliminate the MAD doctrine. No-one would be able to launch nukes at anyone. Conventional war would likely have the same driving factors that it does today. But also, it may not get "car bomb" nukes, so nuclear war still possible, just in a very different mode.
Super high tech: e.g. some crazy quantum detection and elimination of weapons that haven't been fired. This would be terrible, basically the group/state that has this power eliminates its rivals ability to retaliate with a proportional response. They instantly become the major threat in the world, this would destabilize any alliances that they have, no one would believe them if they said that they also disabled their own nukes. This would put the world on the edge of WW3 in a heartbeat.

The US and / or Russia would obtain it ASAP, by hook or crook. Followed rapidly by World War 3
- So conventional warfare?
  
  Your premise is that nuclear warfare is no longer possible, so by default, yes.

It would just be another system they could sell to other countries. That's it.

It's a bit of an oxymoron. A deterrent is about discouraging your opponent from doing something, not preventing them. So kind of by definition it can't be fool proof.
- Does anyone actually want to answer the question?
  Edit:
  If we are just parsing language, here is my meaning:
  prevent the violent force
  
  I think the idea is one of them is convincing someone to not do something they still have the power to do, while the other would be taking that power away completely. There may be a truly foolproof way to disarm a weapon, but there will never be a foolproof way to convince someone of anything due to the unpredictability of people.

Something a lot like this: https://www.youtube.com/watch?v=SpBAFOmdNgU