The 'awrah of a female slave is disagreed upon by the madhabs:
Some scholars hold that her 'awrah is the same as a free woman (everything or everything except face and hands). And some of them have stated that at most the difference is that slaves must not veil their faces unlike free women. They argue that the texts on hijab are general and their apparent wording applies to all women regardless of whether they are free or slaves. And they either consider the evidence of the other madhabs to be weak or interpret it in a way which reconciles it with their own understanding.
Some scholars hold that her 'awrah is nearly the same as that of a free woman but slightly less. One view is that every part of her body is 'awrah except her head and hair. While another view is that every part of her body is 'awrah except her head, neck, forearms and lower legs.
Some scholars hold that her 'awrah is her back, belly and the area from the navel to the knees. This is the predominant view of the Hanafi madhab.
Some scholars hold that her 'awrah is only the area from the navel to the knees. This is the predominant view of the Maliki and Shafi'i madhabs.
Some of those who hold the later of the above views have stated that this was the case during the time of the Prophet ﷺ and Sahaba, but that in later times the slave women should observe greater covering, because of the greater prevalence of vices. (see Hashiyat at-Tahtawi Maraaqi al-Falaah)
The stance of limiting it to between the navel and the knee, or that of extending it to the back and belly is adopted by the majority. Their evidence includes:
إذا زوج أحدكم خادمه عبده أو أجيره فلا ينظر إلى ما دون السرة وفوق الركبة
When one of you marries his female servant to his slave or to his employee, he should not look at her private part below the navel and above the knees.
— Abu Dawud
As when a person gives his slave in marriage, then he can not have intimate relations with her himself. The rule that applies to such a master also extends to others. The version of the hadith in Sunan al-Daraqutni also has the addition that the area between the navel and the knees is her 'awrah.
This is also corroborated by the following (weak) hadith:
من أراد شراء جارية أو اشتراها فلينظر إلى جسدها كله إلا عورتها، وعورتها ما بين معقد إزارها إلى ركبتها
Whoever intends to buy a female slave, let him look at her whole body except her 'awrah, and her 'awrah is what is between the knot of her loincloth and her knees.
— Sunan al-Kubra Bayhaqi
Some have claimed that men used to be disinclined towards slave women belonging to others, which could be because marriage to them is heavily discouraged in the law (see tafsirs of 4:25), and because their children are enslaved. Hence they are compared to men, mahram women and old women. The 'awrah of mahrams is already covered here: What kind of clothes are to be worn around mahrams?
Verse 24:31 allows women to uncover their adornments in front of mahram men, women, their slaves, males having no physical desire and children. When adornments can be shown then the body parts on which those adornments are worn can also be shown. And this implies that the following can be shown: the hair as it is adorned with tiaras, the arms as they are adorned with bracelets, the neck and chest as they are adorned with necklaces and chains, and the lower legs as they are adorned with leglets.
The fact that slave women need to perform labors for their owners, which makes it necessary for them to wear more convenient clothing. And it would be a hardship for them to maintain hijab while fulfilling their duties.
There is evidence that the 'awrah of a slave woman is less than a free woman, so the verses and ahadith on complete hijab do not apply to her. Apart from the ahadith quoted in the first point above, the following are also relevant:
فقال المسلمون إحدى أمهات المؤمنين أو مما ملكت يمينه، فقالوا إن حجبها فهى من أمهات المؤمنين، وإن لم يحجبها فهى مما ملكت يمينه
The Muslims wondered, "Is she (Saffiyya) considered as his wife or his slave girl?" Then they said, "If he orders her to veil herself, she will be one of the mothers of the Believers; but if he does not order her to veil herself, she will be a slave girl."
— Bukhari and Muslim
And the athar:
أنس بن مالك قال: كن إماء عمر رضي الله عنه يخدمننا كاشفات عن شعورهن تضرب ثديهن
Anas bin Malik said: We were served by the slaves of Umar. Their hair was uncovered and their breasts were moving.
— Sunan al-Kubra Bayhaqi
Further, please note the following points:
Firstly, the 'awrah is the minimum area that is obligatory to cover in all circumstances. It does not mean that the norm was that slaves only covered this part and kept everything else naked. For example the 'awrah for men is also from the navel to the knees, but most men do not roam around in loincloths.
Secondly, when some part was not considered 'awrah it gave a concession not just for uncovering but also for the more likely cases such as: when a body part was covered by thin or partial clothing, or when it was not covered by a secondary clothing like a cloak or jilbab because of which its shape was visible, or when it was covered but became uncovered when performing labor such as when bending down to do something.
Thirdly, note that the permission of looking and uncovering is conditional to safety from sexual desire and fitnah. In the absence of such safety it is not permitted to look at any part of the slave, and it would be necessary for the slave to cover herself fully (see Badaa’i’ al-Sanaa’i’ , Mughni Ibn Qudaymah and Majmoo‘ al-Fataawa). Just like it is also forbidden to look at males and mahram women when there is desire or risk of fitnah.
ففيها ثلاثة أوجه: أصحها عورتها كعورة الرجل، والثاني: كعورة الحرة إلا رأسها، فإنه ليس بعورة، والثالث: ما ينكشف في حال خدمتها وتصرفها كالرأس والرقبة والساعد وطرف الساق، فليس بعورة، وما عداه عورة
— Rawdat al-Talibeen
اختلف الفقهاء في عورة الأمة بالنسبة للرجل الأجنبي.فقال المالكية وهو الأصح عند الشافعية: إن عورتها هي ما بين سرتها وركبتها. وقال الحنفية: عورتها مثل عورة الحرة بالنسبة لمحارمها. وقال الحنابلة: إن عورتها كعورة الحرة لا يجوز أن ينظر
منها إلا ما يجوز النظر إليه من الحرة
— Mawsoo’ah al-Fiqhiyyah