As far as i know -and I'm talking about slave woman in general- there's no consensus about this matter in general.
A Muslim can't in any case have a Muslim slave (it's prohibited), only if she/he converted to Islam -later-: he can only marry a slave woman if she became free as the mulk al-yamyn (right hands possessing) is considered to be a stronger relationship than a marriage: this means a Muslim could never marry his own slave but someone else's slave therefore if he wants to marry her he should set her free first! But this also means he can have intercourse with a slave woman -even one who converted to Islam while he is her master- as she is mulk al-yamyn. As a mulk al-yamyn could be considered -as hard as it sounds for us today- as "not having a free will". Note that according to an interpretation of (4:25) mentioned in tafsir al-Qurtubi on (5:5) it is not allowed to marry a slave woman from the people of the book.
On the other Hand for the only today -theoretically- possible case for slavery we have a consensus this means a woman which became prisoner of war is automatically divorced.
In other cases of slavery some scholars say that when a slave couple has been bought by a new master they are automatically divorced.
But most seem to accept that a marriage between slaves is a marriage and by buying them the act of marriage would still hold as an evidence they quoted the Verse 24 in Surat an-Nissa' (4):
And [also prohibited to you are all] married women except those your
right hands possess. [This is] the decree of Allah upon you. And
lawful to you are [all others] beyond these, [provided] that you seek
them [in marriage] with [gifts from] your property, desiring chastity,
not unlawful sexual intercourse. So for whatever you enjoy [of
marriage] from them, give them their due compensation as an
obligation. And there is no blame upon you for what you mutually agree
to beyond the obligation. Indeed, Allah is ever Knowing and Wise.
where the prohibited woman to a man are quoted! They explained that married woman are prohibited to all man except their husbands! This has been quoted by ibn Kathir in his Tafsir and he underlined the 2nd statement
On the other hand a prisoner of war would mean that the woman has fought the Muslims! This would mean such a woman won't be a Muslim because it's not allowed to make a Muslim prisoner of war even in a war between two Muslim sects/countries etc. according to fatwa 8263 here!
If a married woman somehow became slave of a Muslim this would mean she is not a Muslim, as a Muslim can't have (is prohibited to buy) a Muslim slave!
But she could convert to Islam while being a slave of a Muslim.
A slave won't automatically be set free because she/he became Muslim!
Most scholars will accept the marriage of the (bought) slave woman (but not for prisoner of war) as a reason to make her haram for her Muslim master according to the above Verse! Others consider becoming a slave equal to a divorce.
A slave has no free will according Muslim scholars so converting to Islam won't change their status as mulk al-yamyn and the rights of the master (however he can't have intercourse with a slave woman immediately and must wait for her 'Idah, which is her first menses or -if pregnant- the birth of her child). This means they will be at 1st considered as mulk al-yamyn then as believers as it seems. This would mean being a believer or not for a slave still is the same (as it seems) as the master could marry them whit whom he wants or take them for his own use in any way which is halal! So if she became a concubine (sariya) she of curse should guard her private parts for her master!
If the Marriage of a slave couple is considered to be valid then of course the woman should guard her private parts for her spouse only (Again it doesn't matter whether she is a believer or not, but a believer is asked for it according the quoted Verse!)!
Now if the woman (with a valid marriage to a male slave) converted there are 2 possible cases:
- Her husband converted also to Islam in this case the marriage still will be valid and therefore she can/should only have intercourse with her husband.
- If her husband didn't convert then according to shari'a this would mean they will be divorced (a according the rules of shari'a I'dah etc. which i don't know for slave!) in this case her Muslim master could have intercourse with her when the divorce takes effect ('idah) if his conscience allows him to do so!
And Allah knows best