Connie Willis is a novelist, whose interest lies in telling stories (The Doomsday Book features academic historians who conduct primary research via time travel – now there's a thought-provoking conceit) does not require her to ground herself in academic work, and while it's notoriously hard to prove a negative, we can be relatively certain that cases of the sort you're describing did not take place (certainly not to the extent of being "relatively widespread") in the aftermath of the Black Death. That's certainly not to say, however, that cases of imposture did not occur in the medieval and the early modern periods – on the contrary, they seem to have been common – only that the sort of cross-class claims that you're describing would have been very difficult to pull off during the mid-fourteenth century.

There are two major reasons why it would have been pretty nearly impossible to pull off the sort of impostures suggested by this question. One is that even the Black Death – which remains almost certainly the most lethal pandemic known to history – did not come sufficiently close to eradicating the vast swathes of the population that would have been necessary for them to succeed. To be able to successfully take the place of a dead master, or lord, suggests that everyone who could have identified the dead person would have been wiped out by the plague. Even though estimates of mortality in Europe in the period 1347-51 have been drifting back upwards over the past couple of decades – from around 25-30% towards the 60% hypothesised by the modern authority Ole Benedictow – that simply did not occur. In almost every conceivable circumstance, there would have been sufficient tenants, servants and retainers, and surviving family members to make any attempt to assume a dead person's identity implausible.

The second reason why Willis's suggestion makes little sense is that there were (hardly surprisingly) many pretty significant differences between members of the servant class and those they worked for in this period. Education and literacy were the preserve of the wealthiest members of society, and, even allowing for the opportunities there might have been to observe behaviours, the numerous social codes in place – covering everything from manners to forms of dress – would have made it almost impossibly difficult for servants to convincingly impersonate people from a different background, with very different ideas, habits and appearances, in the 1340s. Really, the only way that such an imposture might have succeeded would have been in circumstances that would have made the whole idea fairly pointless; perhaps it might have been easier to make such a claim – then, as at pretty much any other time – by moving to somewhere far distant, not drawing too much attention to oneself, and resisting the temptation to make any legal claims to money and property likely to bring the whole affair to public notice. But, then, why bother to go to such lengths?

I mentioned that there is plenty of evidence for impostures in the medieval/very early modern periods, and perhaps taking a look at a couple of those cases will help us to understand the possibilities and limitations of trying to assume someone else's identity in a period in which there were no identity documents, and relatively few written records of the sort that might be used to prove claims such as these, but also some significant obstacles to fakery of this sort, not least some very restrictive legal obligations and fairly limited geographic mobility. The story that most readily leaps to mind is probably the famous 16th century case of Martin Guerre, a French peasant who – having left his home village to join the royal army and fight in Spain – supposedly returned home eight years later to resume his former life. As Natalie Zemon Davies has shown in her well-known study of the case, the person who actually pitched up in the Pyrenean village of Artigat in 1556 was actually one Arnaud du Tilh. Tilh successfully assumed Martin's identity and lived as him in Artigat for four years. He had a number of advantages in pressing his claims, the most important of which was that Martin's wife, Bertrande, publicly accepted him as her husband, for reasons that historians still argue about; she might have preferred him to her apparently rather oafish spouse; he might have been a better lover; he certainly made it a lot easier for her to undertake the physically arduous job of running her smallholding; and, perhaps not least among the benefits, the imposter helped her to press claims to various parcels of land belonging to Martin's deceased relatives. Tilh also came from a village close to Artigat, and so presumably understood the rhythms and customs of the district; and he had met and received information about Martin from two other men who knew the missing soldier well.

Without the support and (presumably) connivance of Bertrande, it would surely have been impossible for Tilh to push through the claims he made, but, nonetheless, it was scarcely the case that the imposture went unchallenged. Some people in the village doubted the returnee from the outset; Guerre's uncle Pierre tried to persuade Bertrande that her "husband" was not who he claimed to be; a passing soldier who had known Martin Guerre in the army denounced Tilh as an imposter and told the villagers that the real Martin had lost a leg in combat; and there were two trials aimed at proving that Tilh was a fraud, one in 1559 and the other in 1560. In the course of the latter, famously, the real Martin reappeared in court (minus a leg) to prove that all the charges were true, and Tilh was executed for his crimes. All in all, and even without the dramatic final court-room "reveal" provided by the real Martin, we can conclude that Tilh could never have succeeded in making good his claim to be Martin Guerre for more than a few years, and that the main reason he would have failed was that there were too many people in the village, and too many members of Martin's family, who remembered him well enough after eight years to denounce the fraud, even though these people lacked any sort of written evidence that Tilh was an imposter.

Arnaud du Tilh, we ought to note, was attempting something ambitious, but not quite so ambitious as the sort of imposture postulated in your question. He did not claim to be a member of a different class, or to possess a social status very different to that he had been born with. To find an example of that sort of imposture, we need to consider the case of Perkin Warbeck, a pretender to the throne of England, who – after the Battle of Bosworth (1485) resulted in the death of Richard III and the accession of a new dynasty of monarchs in the person of Henry VII – claimed to be Richard of Shrewsbury, the nephew of Richard III, and the younger of two princes who had disappeared while being imprisoned in the Tower of London in 1483.

A couple of circumstances did favour Warbeck in his attempts to press his claim. Richard of Shrewsbury had been only 9 or 10 when he disappeared, whereas Warbeck appeared on the scene only in 1490, aged about 17; vast physical differences between the real boy and the a pretender in what was then early manhood were only to be expected. More significantly, I'm sure, the dead prince, had he actually survived, would have had a stronger dynastic claim to the throne of England than Henry VII did, and the whole point of Warbeck's imposture was to rally support from noble supporters of the House of York who might not care too much about the finer points of his identity if it meant restoration of the power, influence and wealth that Henry's Tudor dynasty had stripped from them. Finally, Warbeck's imposture owed a great deal to the support of foreign magnates who had a political or financial interest in stirring up trouble in England, among them the Holy Roman Emperor, Maximilian I; James IV of Scotland; and Margaret of Burgundy, who was aunt to Richard of Shrewsbury. These supporters not only provided Warbeck with the money, men and supplies with which to press a military claim to the English throne, but also possessed sufficient eminence and power themselves to still at least some of the doubts that certainly did circulate as to "Warbeck"'s true identity.