I've been running debian sid on a spare drive for a while and I really like it, but I question it's stability long term, I don't want to distro hop until I know my next distro WILL work. When people talk about rolling distros like arch or debian sid being unreliable and "breaking" after a "bad update", what do they mean? Would the system just refuse to boot? Would it be more of a minor bug like a part of my DE breaking? In most cases how fixable is this "breakage"? My current main distro is Kubuntu 19.04.

since Sid is where all the new packages get tested before going into testing repo you are more likely to come across bugs.
It is impossible to say how that bug would manifest itself.

but most bugs are reported and fixed quickly.
downgrading a package and setting an ignore of the buggy version is one way around the problem.

Testing is probably thought to be a "safer" rolling distro if you are nervous about being on the bleeding edge.
However, bugs are not fixed quite as quickly as a package has to pass through Sid before getting to testing.

Debian Sid is more stable than most "stable" distro releases. Ubuntu is based on Sid. Debian Stable, in my experience, is rock-solid. I'm not using it at the moment, but I've used it extensively over the years.

Just as with a car, a broken" system can take many forms, depending on which part broke. It might just ride rough, or it might leave you stranded along the road, or something in between.

When I tried Arch, it pushed out a bad kernel update that would not boot. Rebooted and picked the old one, then a few days latter updated things and new kernel got installed. Rebooted and it did not work, and found out the system had removed my older working kernel. So 2 updates in a row resulted in unbootable kernels as the system defaults only kept 2 kernels in /boot.
Is that broken enough for you?

Another example with Gentoo, place I used to work at the lead developer was playing it and used it for production system. A months latter it was impossible to install updates since it was so out of date. The update tool could not handle just a few months without updates.

I've had one Tumbleweed update result in my laptop not being able to boot into the graphical mode (level 5). I could boot to multiuser mode (level 3) and issue startx just fine (though I had to track down an old X startup file to get the window manager up and running). Everything else on the system worked normally. A subsequent update corrected the problem.

There are probably more subtle ways a distribution could go slightly pear-shaped and I'd bet some broken things go completely unnoticed and then fixed in a newer update without users realizing anything had been wrong.

Cheers...

I've been using Sid for years now and the only real issues I have are when Io fail to notice that something important, like the NVIDIA driver, are to be removed as part of the dist-upgrade. Sometimes, as mentioned above, the particular kernel or a specific package may not work and it just requires choosing an older kernel on boot or going without a certain application until the issue is fixed.

There's no clear definition of what that means.
Generally speaking, when fixing whatever is broken would require more work than a reinstall, you could say it's broken for good.
For some people this threshold is significantly lower than for others.
I guess that's a polite way of saying that the people who told you that just didn't know their Linux very well.

The breakage can also come from major upgrades to applications which a rolling distro will toss in with other updates. The OS will boot fine, but your website might be broken because the Joomla update that got pulled in requires you to make changes you were not aware of.
Things like this are more likely with a rolling distro as you need to pay attention to major application updates.

If you are worried about stability, then you should be using a distro that has long term support. A rolling distro is for people that want the latest and greatest and are ready to fix things when something breaks.

That raises another question. Which is typically more reliable; semi-annual upgrades, or rolling release?

The semi-annual upgrades will go thru some testing to ensure the upgrade works, rolling release not so much.
LTS versions are even more stable since they are just supplying security and bug fixes for the years they are covered, not new versions of apps.