Concealing people’s sins is a matter that is subject to further discussion

If it is proven that the woman actually committed a sin with
this man, then if she was not known for doing that, and it was an isolated
incident and an error on her part, then it is better to conceal her sin and
not report the matter to the authorities, whilst advising her, reminding
her, calling her to Allah, and explaining to her the seriousness of what she
did and what may result from it of negative consequences. If she repents,
regrets it, asks Allah for forgiveness and promises not to do such a thing
again, then it is recommended to conceal her mistake.

It was narrated that Abu Hurayrah (may Allah be pleased with
him) said: The Messenger of Allah (blessings and peace of Allah be upon him)
said: “Whoever removes a worldly hardship from a believer, Allah will remove
one of the hardships of the Day of Resurrection from him. Whoever grants
respite to (a debtor) who is in difficulty, Allah will grant him relief in
this world and in the Hereafter. Whoever conceals (the fault of) a Muslim in
this world, Allah will conceal him (his faults) in this world and in the
Hereafter. Allah will help a person so long as he is helping his brother.”

Narrated by Muslim (2699).

But if this woman is known for committing evil and immoral
deeds, and persists in that, and does not give any sign of repenting or
regretting it, then undoubtedly it is better to report her to the
authorities. In fact that may be obligatory, in order to discipline her and
put a stop to what she is doing, so that she will not think of doing such a
thing ever again.

Ibn Rajab (may Allah have mercy on him) said, after quoting a
number of hadiths that speak of concealing a person’s sins and not exposing
him to scandal:

However it should be noted that people are of two types:

One type
is the person whose situation is concealed and he is not known to be
committing any sin. In that case, if he slips up or falls into error, it is
not permissible to expose him or disclose his error, or to speak about it,
because that is unlawful backbiting. This is the one concerning whom these
texts were narrated, and concerning that Allah, may He be exalted, says
(interpretation of the meaning):

“Verily, those who like that (the crime of) illegal sexual
intercourse should be propagated among those who believe, they will have a
painful torment in this world and in the Hereafter”

[an-Noor 24:19].

What is meant is spreading news of shameful deeds on the part
of a believer who had been concealing his error, or who had been accused of
that when in fact she was innocent of it, as in the story of al-ifk (the
slander against ‘Aa’ishah (may Allah be pleased with her)).

One of the righteous ministers said to one of those who were
striving to enjoin what is right and proper: strive hard to conceal the
faults of sinners, for broadcasting their sins brings shame to the Muslims,
and the matters which are most deserving of being concealed are faults. If
someone like this comes expressing repentance and regret, and admitting to a
sin that is deserving of a hadd punishment, but he does not explain what it
is, he should not be asked to explain what it is; rather he should be
instructed to go back and conceal his sin, as the Prophet (blessings and
peace of Allah be upon him) instructed Maa‘iz and al-Ghaamidiyyah [two
believers who each eventually admitted having committed zina] to do; and as
the one who came and said, “I have committed a sin that is deserving of a
hadd punishment, so carry it out on me” was not asked for details. If such a
person is caught for committing an offence, but it has not been reported to
the authorities, intercession should be made for him so that news of it will
not reach the authorities.

Concerning a similar case it says in a hadith narrated from
the Prophet (blessings and peace of Allah be upon him): “Overlook mistakes
committed by people of good character”. This was narrated by Abu Dawood and
an-Nasaa’i from the hadith of ‘Aa’ishah.

The second type
is the person is known for committing sins and commits them openly, and does
not care what kind of sins he commits or what is said about him. This is the
evildoer who broadcasts his sins, and speaking ill of him is not regarded as
backbiting, as was stated by al-Hasan al-Basri and others. In this case
there is nothing wrong with investigating what he does, so that the hadd
punishments may be carried out on him. This was stated clearly by one of our
companions, and he quoted as evidence the words of the Prophet (blessings
and peace of Allah be upon him: “Tomorrow go to this woman, O Unays, and if
she confesses, then stone her.” In such a case, there is no intercession for
the individual if he is captured, even if the matter is not referred to the
authorities. Rather he should be kept until the hadd punishment is carried
out on him, so as to put a stop to his evil and deter others like him.

Maalik said: If a person is not known to bother people, and
it was rather a mistake on his part, then there is nothing wrong with
intercession being made for him so long as the matter has not reached the
authorities. As for the one who is well-known for his evil and mischief, I
do not like for anyone to intercede for him; rather he should be kept until
the hadd punishment is carried out on him. This was narrated by Ibn al-Mundhir
and others…

End quote from Jaami‘ al-‘Uloom wa’l-Hikam (1/341).

Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said:
What is meant by concealment is concealing the fault, but concealment cannot
be praiseworthy unless it serves an interest and does not lead to any
negative consequences. For example, if an offender commits an offence, we
would not conceal his deed if he is known for committing evil and mischief,
but if a man is outwardly righteous, then he does something that is not
permissible, in that case it is required to conceal his deed. So with regard
to concealment, we should see if it serves an interest. So if a person is
known for his evil and mischief, it is not appropriate to conceal his deeds,
whereas if a man is outwardly righteous, but he does something wrong, this
is the one whose deed it is Sunnah to conceal.

End quote from Sharh al-Arba‘een an-Nawawiyyah (1/172)

And Allah knows best.