This is also a detailed reply to the OP's answer
The post linked in the comments: Stack Exchange doesn't allow me to answer protected questions because I gave away earned rep in bounties was posted in 2014, and the protected message was the following
[emphasis in bold mine]
Thank you for your interest in this question. Because it has attracted low quality answers, posting an answer now requires 10 reputation on this site.
The OP in the older post offered 350 reputation points (henceforth ‘rep’) in a bounty after earning 270 points which added to their bonus made a total of 370. Therefore, the OP was left with 20 rep, which they believed was sufficient to answer a protected question but the system determined that those points had not been earned. Remember, the OP's earned rep was 270 but their bounty was 350 which meant 80 rep came from their bonus.
I don't know anything about AI but I imagine that it looked at the user's profile, saw the user had been awarded 100 bonus and had 20 rep remaining. To AI (I guess) it meant the user hadn't earned the necessary 10 reputation points to answer a protected question.
Nevertheless, the older message was indeed ambiguous. It suggested that users only needed 10 rep, when in actual fact users with the 100 bonus had to "win" or "earn" 10 rep on the site by receiving upvotes on their contributions or by having their suggested edits approved (2 rep).
Personally, I find the new notice clearer and correct. If a user has not earned at least 10 rep, they cannot answer a protected question. An avid user with the association bonus should understand what the following means: “Earn 10 reputation in order to answer this question.”
However, inexplicably, there is no mention of the association bonus in the notice. And there is no mention of the association bonus in the privileges page, which I do not understand.
What are protected questions?
Once you’ve earned 10 reputation points from participating on this site, you’ll be able to answer a protected question.
What does the MSE FAQ post say about this issue?
"Users with 10 or more reputation can answer a protected question. However, the +100 account association bonus is ignored for this check2, so users with the association bonus require 110 reputation to answer protected questions. In other words, all users must have earned 10 or more reputation on that specific site to answer a protected question."
2 On per-site metas, this restriction does not apply; if you have the association bonus, you can answer protected questions on per-site metas without needing to earn 10 rep on the main site first (provided your reputation on the main site hasn't dropped below 10).
No mention whatsoever that a user has to earn back the rep lost from the association bonus, so when @Sonic's answer suggests the wording in the notice be modified to
Or, if a user has earned the association bonus and has 71 reputation (they put up a 50-rep bounty and received two upvotes):
[emphasis in bold mine]
You need 39 more reputation to answer this question. A total of 10 reputation is required to answer this question, to protect this question from spam and non-answer activity (the association bonus does not count).
I still retain that a user needs only 10 rep before they can answer a protected question.
I am a member of SO, I have the association bonus but in all these years I have only increased my reputation by seven points, I need an extra 3 rep to answer a protected question. As a result, when I visit a protected question on Stack Overflow I am greeted by the following notice.
Weirdly there is no mention of my association bonus, but the notice makes it clear that I am not allowed to answer unless I have earned 10 reputation. The fact only 3 more rep is necessary for me is inconsequential.
Improve "Protected Question" message with regard to rep gained through Association Bonus
Make reputation message when answering protected questions less ambiguous
Stack Exchange doesn't allow me to answer protected questions because I gave away earned rep in bounties
Why is the Association Bonus ignored when trying to answer a protected question?