I understand this was asked similarly before, but you can see that the answer did not touch this point specifically. What economical / social / political causes allowed for the shift between being able to sell a person and working on a field of land a few days a week to pay the landlord?
It's been about a year since I did anything on this topic so forgive me for any mistakes I make in terms of the Historiography or nuances on the topic. The shift away from systems of slavery occurs far later than one might expect, it is around the year 1000 Pierre Bonnaisse (1) identities slavery as having ended in France, although we must remember even after the shift towards serfdom slavery still existed into the high middle ages in the form of galley slavery and eventually economic chattel slavery imported from Syria by the Genoans.(2)
The nature of the shift away from slavery towards serfdom occurs slowly over a long time making it a favoured topic by the Annales school, contemporary studies look more towards the ideas of "unfreedom" and "freedom" which are far more useful terms in deriving information about the transition. I'll largely base this off my reading of Alice Rio's book Slavery after Rome.(3)
What is Medieval Slavery: In brief I don't think medieval slavery is so much to do with selling or buying people as later slavery is, but to do with cultural ideas of debt and punishment. Slavery took different forms such as:
Capture and resale: Typically a goal of Viking/Islamic raids and unsurprisingly disliked in Christian sources (Life of St.Wulfstan for example).(4) Western Christians also partook in this form of slavery too, but as a bi-product of conquests like the expansion of Charlemagne's empire into Slavic lands or the instability of the Heptarchy period in England, slaves takenin this way were moved and planted on estates as labourers.(3) However, this form of slavery shouldn't be emphasised too much as it is typically seen on Scandinavian, Islamic and Pagan peripheries and remains unsourced in western documents.(3)
Debt: A favourite term of economist David Graeber, this explains slavery on local levels where figures may willingly sell themselves into temporary slavery in order to pay off unpayable debts to someone else in the community.(3) I'm not hugely familiar with the impact of this on ones family but I would imagine they also become slaves until the debt is payed. This is where "unfreedom" becomes useful as people in this position are subservient and slaves, but still partake in the community and can have ambiguous social statuses, in general however they're unfree.(5)
Punishment: Very similar to debt slavery this was paying off a debt to legitimate legal authority via temporary enslavement.(3)
Why Did Slavery "end" in Medieval Europe:
Feudal Impact: The "feudal revolution" led to a shifting role of the general peasant and in general symbolised a shift from paying tribute to those above you but towards a system of obligation that is feudalism. Seen in the ideas of the school Auxerre and King Alfred the Great there's a general shift towards the notions of "three orders" and mutual obligations in the 9th century which eroded some of the practical and social reasons for slavery.(6) Lords are quite likely to grant manumission/freedom to slaves and even grant them property to live on which allows them direct access to their labour, rather than having the intermediate access via a slave owner.(7) This may have been to do with the collapse of the Carolingian empire with Charles the Fat in 888 into many polities as the more personalised feudal politics that followed encouraged a shift away from slavery for aforementioned reasons.(8) In England we can see this following the Norman Conquest of 1066 which largely ended the collapsing practice for good, in the Doomsday Book we see a lot of examples of slaves freed by their new lords and added to the general collective of serfdom who incidentally may have become increasingly "unfree" as a result.(9)
Church Impact: Surprisingly church impact was initially limited in the ending of slavery and permitted rural slavery beyond the nobles (in England) as they couldn't as effectively monopolise the labour of serfs as effectively as the nobles.(10) Guy Bois was increasingly cynical about the church's role in ending slavery, citing examples such as St.Augustine who called it a "temporal punishment" and their Christian pushing of acceptance of ones place in this life as all could be redeemed in Heaven.(11) Nonetheless the church doubtless had social impact, in England and France it shows an increasing intolerance towards slavery towards the millennium, something that likely took a while to come into effect (the works of Aelfric of Eynsham, Wulfstan of York and Wulfstan of Worchester in the context of England).
Social Impact: As mentioned before, debt slavery (alongside penal and self sale) were common in early medieval communities but one could remain a slave and generate a social standing within a village. One of the most important sources for this is the example of the Judgement of Courtisols in 847, in which serfs in Chalons-sur-Marne vouch for the serf status of several slaves in the village (until some village elders attest against it).(12) This implies the status of slavery in a social context was malleable and in the absence of personally aware authority people could work or earn their way out of slavery, something that plausibly occurred in times of chaos (which paradoxically may have created more slaves too such as after the Danish invasion of England in the early 11th century).
Conclusion: In conclusion the question is incredibly difficult to answer, the end of slavery in the early middle ages is more of a transitional period towards general serf-ly "unfreedom" more than any form of mass liberation or radical shift in thinking. This is a rather Anglo-centric answer unfortunately, although I don't know much about the ends of slavery in places beyond England or France, ultimately, it is just important to recognise that slavery was malleable and transitionary, rather than enshrined institutionally to any serious degree, the names for "serfs" and "peasants" in of themselves vary and aren't codified, it is dependent upon local social relations to function.
General Sources (I don't know how to cite on Reddit):