The term "failbreak" is used to mean one or both of two things: an incomplete or otherwise flawed jailbreak that cannot run Cydia Substrate properly, or a jailbreak that cannot be released to the public for some reason (whether or not that jailbreak is complete). Some "failbreaks" are both incomplete and cannot be released to the public. Sometimes people also call fake jailbreaks "failbreaks". Since this word has multiple possible meanings, it's confusing to try to use it in conversation, so it's best to avoid it.
saurik has said that "the term was actually first used years ago by chpwn on a released jailbreak as there was something wrong with it that caused Substrate to only work in some processes; I was then later using it with regards to jailbreaks where the kernel patches didn't support the various memory protection changes required by C Substrate. I provide a tool called 'vmcheck' that people developing jailbreaks use to 'unit test' their patches, and when it fails... well, that's a 'failbreak'."
This term came up again when chpwn showed a screenshot of his new iPhone 5 running Cydia shortly after its launch on 19 September 2012. He explained this as "the “failbreak” is for jailbreak developers (e.g. @iphone_dev, @chronicdevteam, etc)." On 19 October 2012, planetbeing tweeted that he upgraded the "failbreak" with a kernel exploit so that tweaks actually work on the iPhone 5, to make it "almost a full tethered jailbreak."
In March 2015, chpwn said "I open sourced the code for the old ‘failbreak’ from around iOS 6.0. (The exploits involved are all fixed now.) http://github.com/grp/amfi_interpose"
- iOS 4.2.1 (Jailbreak Monte)
- Access to iOS 4.2 beta 3 for device
- iOS 6.x on A5, A5 Rev A A5X, A6 and A6X
- Apple Developer account required
- Developers under NDA