Let's say that X knows a person B, who is an alcoholic and beats his wife.
X does not report B to anyone who could take action on B. He chooses to do nothing. Eventually, B's wife is killed by B in a domestic argument.
B is later tried in court, but because there are not enough witnesses, B is found innocent. X chooses not to testify.
B later on marries someone else, who X knows, but X still doesn't tell her about B's character.
Is X being sinful through inaction?
Note that I'll only answer your post according the title as for the example case maybe an elaboration would be needed and as far as I can tell the other answer is referring to it and solving it to some extent!
Inaction is indeed a sin as Allah prohibits hiding the the truth (see for example 2:42). And therefore in an other place in the Quran HE says (91:14-15):
But they denied him and hamstrung her.
In fact they denied their Prophet (or his teachings) but it was not all of them whom hamstrung the she-camel but one or some of them only. But Allah's punishment overtook all of them as those who didn't stop this sinful act have committed the sin of not forbidding wrong nor enjoined good as they should! Read also this statement about similar cases from al-Muwatta':
"Some say that Allah the Blessed, the Exalted, will not punish the many for the wrong action of the few. However, when the objectionable action is committed openly, then they all deserve to be punished."
That's why Allah says later:
So their Lord brought down upon them destruction for their sin and made it equal [upon all of them]. (14) And He does not fear the consequence thereof.
Also read (5:77-81).
In the Quran and sunnah there's a strong emphasize of the importance of enjoining good and forbidding wrong الأمر بالمَعْرُوف والنَهي عن المُنْكَر. Read for example verses such as 3:104, 3:114 and these two verses of surat at-Tawbah which make a comparison between the hypocrites and disbelievers on one side and the believers on the other. And in the sunnah you may find some ahadith like in (here one version from) sahih al-Bukahri, Jami' at-Tirmdihi (which goes ahead with the statement from above), sunan ibn Majah and an other hadith from Jami' at-Tirmdihi. And the famous hadith which is among the 40 of Imam an-Nawawi (see for example in sahih Muslim) saying:
He who amongst you sees something abominable should modify it with the help of his hand; and if he has not strength enough to do it, then he should do it with his tongue, and if he has not strength enough to do it, (even) then he should (abhor it) from his heart, and that is the least of faith.
Which has been explained as follows: people in changing or modifying or stopping a wrong or abominable act are levels. Everybody should do the modification according his own possibilities. For example changing by acting (with the help of his hand) can mostly be done by authorities only, changing by pointing at it (with his tongue) can be done by scholars and laymen and anybody who has strong enough faith and courage to do so and for those who have not this courage remains the change in their hearts (by rejecting a sinful act). Now the question could be is this last option halal if nobody acts? No it wouldn't be as enjoining what is good and forbidding what is evil are two of the duties of shari’a (For see details this fatwa).
The situation described in is absolutely a wrong thing by X, but their can be circumstances where X is doing the right thing in some parts.
Let's analyze this story in parts.
X knows B who is alcoholic and beats his wife, now he does not report it to any one "who could have taken some action"...
Assuming by someone here it means some relative or elder of the neighbourhood who have some influence on B, In this part X is wrong, why? Because, helping the muslim is part of the faith. Though first reason would be amar bil maroof wa nahi anil munkir which is a duty:
"The Believers, men and women, are protectors one of another: they enjoin what is just, and forbid what is evil: they observe regular prayers, practice regular charity, and obey Allah and His Messenger..." (at-Tawba, 9/71)
Here X didn't performed his duty. And second reason not helping oppressed and oppressed muslim brother, as hadees states:
Narrated Anas: Allah's Apostle said, "Help your brother, whether he is an oppressor or he is an oppressed one. People asked, "O Allah's Apostle! It is alright to help him if he is oppressed, but how should we help him if he is an oppressor?" The Prophet said, "By preventing him from oppressing others."
Here X had to help that couple, which he didn't. So, obviously in this part, X is not following at-least 2 commandments of islam.
Than, next part: Eventually, B's wife is killed by B in a domestic argument. B is later tried in court, but because there are not enough witnesses, B is found innocent. X chooses not to testify.
Now here is a BIG problem...
Islam orders believers to testify what they know even without being asked for it.
وَلَا تَلْبِسُوا الْحَقَّ بِالْبَاطِلِ وَتَكْتُمُوا الْحَقَّ وَأَنتُمْ تَعْلَمُونَ
And cover not Truth with falsehood, nor conceal the Truth when ye know (what it is). Quran 2/42
وَلَا تَكْتُمُوا الشَّهَادَةَ ۚ وَمَن يَكْتُمْهَا فَإِنَّهُ آثِمٌ قَلْبُهُ ۗ وَاللَّهُ بِمَا تَعْمَلُونَ عَلِيمٌ
And do not conceal testimony, for whoever conceals it - his heart is indeed sinful, and Allah is Knowing of what you do. quran 2/283
There are many other verses and references for this issue, for now these 2 ayahs are clear and conclusive, not giving testimony when you know it can give justice to someone, is a big sin.
Now last part:
B later on marries someone else, who X knows, but X still doesn't tell her about B's character.
Firstly, it was X's duty to let the other person know about the character of B before marriage, because it is like saving someone from being oppressed, because B is likely to do same again. If he knew all the happenings about marriage/proposal etc and he could have easily told them, it was his duty of the category of well wishing/helping muslims which is an integral part of islam.
Secondly, now after the marriage if their life is ok now, and there's nothing like the first one, like domestic violence or anything, in short they are having normal married life, than its better not to tell his wife anything. But, if situation is like before, and violence has been started, he can tell her seeing all the scenario and results. With the same reason of well wishing for muslims.
PS: I am not a mufti, still if i was X, i was on this stage i would have testified now on this stage, and had reopened the case. Because i think its better to clear your mistakes rather than having sinful heart for the rest of the life and for the akhirah. But it depends on the situation anyway.
