I love this question because it starts out seemingly negative (how do you lose a city?!) but ends up someplace positive: people can be amazingly resourceful.
Have you seen a building torn down or imploded today so something else can be built in its place? The building becomes first a pile of rubble, then a giant hole. We haul away the rubble that was the building and its foundation. Lots of it ends up in landfills. The useful parts--wires are the big one cited--might be sorted and sold as scrap.
Premodern building demolition in Europe was all about reusing what was reuseable, of course. One famous example is the piecemealing of Roman stone structures in early medieval Britain. Notre-Dame de Paris has Roman-era stone pieces in part of its foundation, and possibly some Carolingian as well. And of course, as I talk about in this cool earlier answer the medieval city of Rome itself was largely built into or out of old Roman buildings!
But lacking a real-life Merlin to engineer exotic contraptions that could haul heavy building materials from Ireland to Stonehenge, medieval people tended to skip that "gaping hole" stage. It was logistically just plain easier to salvage what could be salvaged and then build the ground up to smooth over ruins to the point you could build a new structure.
In fact, this could become part of the building itself. In one type of construction, the ground was leveled off by packing in dirt and rubble, and the stone walls were constructed right on top of it. Otherwise, a building might be constructed around stone-and-mortar piers. A foundation trench would be dug, the pier constructed up to ground level, and the space around it packed in. From both France (Cluny) and England (London), there is evidence that in some places the use of piers was practiced in religious building in the early Middle Ages and then adopted for secular construction from the twelfth century or so.
(John Schofield's excellent article "The Construction of Medieval and Tudor Houses in London" is available online, for anyone interested in understandable explanations of medieval construction beyond lists of basic materials. The PDF is 41MB; caveat clickor.)
So essentially, there's not really an intermediary stage if a particular space is going to be continuously inhabited. For truly abandoned sites, like the cities wasted by the Mongols that didn't re-attracted residents until new settlers showed up centuries later, probably one could witness ruins half-buried in dirt deposited by wind and water. /u/kookingpot has a fabulous and fascinating post on geoarchaeology that discusses the natural burial of old cities as well as human-caused.
As to the lack of memory? If the buildings were also demolished in the Middle Ages or the early early modern era, it doesn't surprise me at all that there's no modern memory or record of what stood there. That's just not the kind of thing recorded in city archives. We might know from tax records or a parish register or a will that someone was a shoemaker, or a draper of secondhand fabric. We don't have a street address or the deed to a building.
And medieval (and early modern) people were pretty used to rebuilding. Medieval peasants, according to Barbara Hanawalt, built and rebuilt houses fairly frequently. In cities, fires frequently gave people no choice but to rebuild. Fear of fire was rampant in the Middle Ages; in handbooks for priests to help them instruct people in not sinning, arson is right next to murder as the two worst sins of Wrath. When the libri mechanorum gets going as a genre of literature in the 15th-16th centuries, featuring wondrous extrapolations of existing technology into helpful new machines, firefighting engines are among the most prominent. (Here's one idea from 1594). That's to say: medieval people's experience of everyday architecture was that it was necessarily transient.
Which always makes me wonder what medieval pilgrims to a splendor like Sainte-Chapelle thought. Did they believe it would last forever? Or did they see it crumbling into decay like, they believed, all matter in a fallen world ultimately must?
You might find u/Tiako 's top comment from this thread 4 days ago to be an answer to your question;
If you don't mind me asking, what city do you live in? I'd like to read about the excavation and their findings.
A related question, if I may. I’m a classicist and am very familiar with the archaeological remains of Rome. But I’ve always been fascinated by life among the ruins. It’s a standard comment that “Rome turned away from the forum and towards the Vatican” following the fall of the western Empire. But the ruins must have been reused. I know the forum was later used for grazing, and there’s evidence of people using different ruins for stables and livestock and what’s been termed the “rusticfication” of the city. But beyond Christians reusing the ancient monuments what other evidence do we have of how people interacted with these ruined structures?
One of the better examples of this is the city of Rome, where you have different archaeological layers each representing a different time period in the cities development.
In the centuries after the fall of Rome, after repeated assaults from barbarians and disease took their toll, many of the inhabitants left the city. This was a metropolitan city of over a million people at its height, and by the 8th century there were less than 10,000 inhabitants living there. Since the city was so large and had been built on the assumption that there would always be slaves to care for it, it was very susceptible to ruin once there was no one left to care for the sewage and drainage systems in the city.
The Tiber floods every year (until the modern Italians built 50ft tall retaining walls to keep the water at bay). Every year this flood would deposit a millimeter of silt and detritus all over the low lying areas of the city. The slaves would come and clean it up and life returned to normal quickly thereafter.
Without slaves and a general population to care for the city, these annual floods continued to deposit millimeter after millimeter of sediment century after century. Eventually people found themselves walking down a few flights of stairs to get to church, because it had been built 400 years prior and the ground level had risen 6 ft since then.
The best example of this is the Basilica of San Clemente in Rome. Built near the colosseum, the church sits 6 ft below modern ground level, and was built in the 900s. In the 19th century the church sponsored an excavation beneath the building and the original church from 4th century ad was uncovered. They had money left over so they kept digging and uncovered a pagan temple from the 1st century fright below that original church.
As the ground level rose around the church eventually they decided to fill in the original church with dirt, and build the new one on top. You can still see where the frescos were chopped in half as they removed the roof of the church to build the new one.
Rome may be a unique situation to your question but thought it fit your area of interest well