I don't really think we need to be doing anything more than what we are already doing.
There is question protection which prevents members with less than 10 rep. from answering a question that attracts low-quality answers from people who do not understand the standards. There is also question closure which prevents anybody from answering it if it is so bad that we suppose nobody should even be trying to answer it yet. If answers were written to such an especially bad question, that has a negative as this once did, deletion votes on the question can be cast by trusted users and any reputation gains or losses will be reversed, which more or less makes it a waste of time to have bothered answering. Finally, as a last resort, people who answer a question before it is established that the question meets our standards are taking a slight risk, because if it is edited to meet our standards their answer may very well be invalidated. In that case, voting against the answer may also a valid option, although you would need to reserve your vote because strictly speaking, we only have a few minutes to change our mind about a vote once it has been cast, unless the answer is edited.
Some of these mechanisms may need a little tweaking to work optimally, but I do not think we can control that at the local level, so I do not think we need to be doing anything more than what we are already doing, and I fear that it may be harmful to the website. Although we do insist upon having good questions, this is a secondary concern that is mostly just a means to an end for us, and that end is having good answers. You can read more about the general philosophy in Jeff Atwood's Optimizing for Pearls, Not Sand.
However, if we can skip a step and get a high-quality answer, even to a bad question, that is at least of some value. I want you to pay special mind to our original research standard: The general reference standard described in Are Some Questions Too Simple? and how the chart therein affords us every opportunity to answer a question if the answer can be of any use or interest: There are three forks with "Answer the Question" ending in a mostly subjective test, and it is only when all three forks fail that are we recommended to close it as "General Referenece" and even if it should be closed, it is generally left to community discretion to decide if it actually will be.
My fear is that we already have adequate means to prevent bad answers to questions if we should so choose to use them, so all that remains to be done is to preempt good answers to bad questions, which is actually counterproductive to our ultimate goal:
With your help, we're working together to build a library of detailed answers to every question about English language and usage.—Our Tour
Aside from that, which questions are up to our standards is actually a highly debatable matter. We may actually disagree on which topics are so bad as to which merit a closure reason. Although I agree this question is not up to our current standards, I could not disagree more regarding the reason for that:
You have suggested that the questioner should a thesaurus, which is often a reasonable request. Yes, I understand: We don't just want people copying and pasting the options out of Roget's 21st Century Thesaurus as shown on thesaurus.com with no further explanation regarding why a word is a good option. "Foox and fooy are synonyms, so you can use foox instead of fooy" is an utterly useless and error-prone answer that could have been more easily found without the need for human intervention.
However, the thesaurus is a somewhat peculiar tool in regards to single-word-requests, because people can only use it if they already know an applicable word. If a person does not propose a synonym, then the question can not be answered by a thesaurus, as the applicability of either suggestion has to be proven in the first place, which leads to a somewhat higher quality answer than the aforementioned use foox instead of fooy example I just now gave.
What is moreover is that it does not constitute an adequate proof to suggest two words are synonyms when the questioner does not even know if either of the words is applicable. The request you are making is not only effectively impossible, but would fail to improve the answers to the question in my opinion, so there are only two options as far as I am concerned:
The question should never have been closed as off-topic in the first place because it can not be answered by "a commonly available reference" and so such closure serves no purpose.
The question is bad because it is otherwise off-topic, so even if a thesaurus is checked, it should remain closed.
I would like to emphasize that I am not casting judgement upon whether the question should be open or closed here. I am merely stating that I disagree with your rationale regarding why it is noncompliant with our standards, and what can be done to make it standards compliant to make a point: There is no safe method to certainly determine if a question is standards compliant or not other than through community consensus, as established by the question's closure status, so we probably should not be penalizing answerers for making that discretionary call by answering still open questions, which are the only sort of questions that they even can (or at least should be able to) answer.