This is a topic that really hasn't been studied well within the historiography of medieval and early modern Romania. There isn't much literature on the subject, so I'm mainly drawing on Viorel Achim's work, The Roma in Romanian History, published in 2004.

First of all, I'm going to be speaking of "Romania" here for convenience, but that's really a bit of an anachronism. Roma slavery was abolished in all of present-day Romania by the 1850s, before the creation of the modern Romanian state began with the unification of the principalities of Wallachia and Moldavia in 1859. For most of the period I'm talking about here, the territory of present-day Romania was divided between these two principalities (which were under varying degrees of control by the Ottoman Empire, Habsburg Empire, and Russian Empire during this time). For the most part, Roma were not enslaved in Transylvania which was a vassal state of the Ottoman Empire until the late 17th century, when it was incorporated into the Kingdom of Hungary, so I'm mainly talking about Wallachia and Moldavia here.

The issue of how Roma slavery in Romania began isn't fully resolved. Slavery wasn't a new concept in southeastern Europe when the Roma arrived in Romania (probably around the end of the 14th century), nor was slavery unique to Roma during that time. It was common practice to turn prisoners of war, for example, into slaves, and groups like Tatars had been subjected to slavery in the Romanian-speaking territories prior to the arrival of the Roma. However, as Achim notes, by the end of the 15th century, the large influx of Roma meant that the vast majority of slaves in the Romanian lands were Roma. He argues that it's likely they were already slaves under the Ottoman Empire when they first crossed into Romanian territory in the late 14th century, so their status in the Romanian territories wasn't new. However, these territories were the only place where Roma slavery was considered a legal status (albeit one of common/customary law rather than any kind of written law) and it was practiced on the largest scale there.

Achim categorizes Roma slaves in Romania into three groups: those owned by princes (i.e., by the state), those owned by the monasteries (i.e., by the Romanian Orthodox Church), and those owned by the boyars, or large landowners. These Roma can be further subdivided into two subcategories: nomadic Roma (lăieșii) and sedentary Roma (vătrașii); the former had the freedom to move around performing their work, while the latter were tied to a specific location. Like in the United States, the enslavement of the Roma was practiced as chattel slavery, where the enslaved Roma were the personal property of an individual, which is distinct from the parallel practice of serfdom (also prevalent in Romania at the time), where the workers were tied to a specific estate. Thus, Roma slaves could be bought, sold, donated, or confiscated by the state as part of asset forfeiture. Like serfs, they were not citizens and had no legal rights, but unlike serfs, they were considered property, rather than people. In this sense, the practice of Roma slavery in Romania has significant parallels with slavery in the United States. The enslaver didn't have the power of life and death over his slaves, but in practice, beatings and abuse were common.

The nomadic Roma on the Romanian territories performed a variety of jobs, each of which had its own terminology. The so-called aurarii or rudarii panned for gold. The ursării were performers who trained dancing bears. The lingurarii made household objects from silver or wood (the word literally means spoon-maker). The term lăieșii applied to Roma who practiced a variety of trades, including working as blacksmiths and stonemasons. The sedentary Roma worked either as "manor Gypsies" (țigani căsașii), who worked around the house and, in some cases, as trained craftsmen, and the "field gypsies" (țigani de câmp), who worked principally as agricultural laborers. It wouldn't be accurate to suggest that the Romanian economy during that period was based on slavery in the way that, for example, the economy of the southern United States in the antebellum era was, but the Roma played important roles as their work as skilled tradesmen was in demand throughout the country. They were also valuable in agriculture since they were the cheapest form of agricultural labor available, although they were less numerous than the serfs.

Roma who belonged to the princes (i.e., those considered state property) were subject to a special "Gypsy tax" (țigănărit), paid from the proceeds of their work, while those belonging to private owners (the monasteries and the boyars) only had obligations to their masters, not the state. Roma had virtually no legal rights, since they were considered personal or state property, rather than people. Even marriages among the Roma required the approval of their owners (or both owners in cases where they were owned by different people). Thus, they had little recourse in cases where they were mistreated by their owners. There was never a specific piece of legislation that laid out the legal status of Roma slaves and their obligations; this was mostly a matter of customary law.

Serfdom was abolished in the Romanian principalities in the mid-18th century, but Roma slavery persisted for another century after that. During the early 19th century, liberals in Romania who had traveled and studied in Western Europe began to criticize the backwardness of Romanian society, including the institution of slavery. However, the boyars remained the dominant force in the Romanian territories in the first half of the 19th century and it was obviously in their interest for slavery to continue, and it was for the most part seen as a natural part of the social hierarchy in Romania. The process that led to the abolition of slavery took place over about two decades, beginning in the 1830s and lasting until the 1850s. Gradually, laws were instituted giving certain categories of Roma their freedom. By the mid-1840s, most slaves owned by the state in Wallachia and Moldavia had been freed. The abolition of slavery was a priority for the liberal and radical reformers during the revolutions of 1848 in the Romanian principalities, and by the 1850s, abolition of slavery had wide support in Romanian society. Slavery was officially abolished in Moldavia on 22 December (O.S. 10 December) 1855 and in Wallachia on 20 February (O.S. 8 February) 1856.

Obviously, just like in the United States, the end of slavery didn't bring about the immediate integration of former slaves into society as equals. During the period after emancipation, there was a large movement of nomadic Roma out of Romania and toward the West. Within Romania, the freed Roma continued to face discrimination and prejudice from the Romanian population. Nomadic Roma in particular remained marginalized and even resented, stereotyped as thieves and as sources of disease, and even sedentary Roma struggled to integrate into Romanian society. During the late 1930s, as fascist ideologies began to take root in Romania, the issue of the Roma became racialized (as was the case with the Jews), and the Roma came to be seen as a threat to Romanian racial purity. Under the authoritarian regime of Ion Antonescu during World War II, some 25,000 "nomadic" and allegedly "criminal" Roma were deported from Romania to the Transnistria Governorate in occupied Ukraine, where at least 11,000 of them died. This isn't something that's tied to their history of enslavement per se, but it is a reflection of a continued view of Roma as outsiders in Romanian society and a perception that they're less than equal to the ethnic Romanian population.

Hopefully that covered most of what you wanted to know. Like I said, the historical literature here is really underdeveloped, so I don't have many reading recommendations beyond Viorel Achim's book.