In the past, these cycles were regional. As Rome fell in the Mediterranean, the Maya rose in Central America, and so on; the setbacks were local, the overall experiment kept going. But now the 10,000-year bets all rest on a single throw.
In essence, the "fall" of the Roman Empire to a contemporary of that age depended a great deal on where they were and their status in the world. On the great villas of the Italian Campagna, the seasons rolled on without a hitch. The local overseer may have been representing an Ostrogoth, then a Lombard duke, then a Christian bishop, but the rhythm of life and the horizons of the imagined world remained the same. Even in the decayed cities of Italy consuls were still elected. In Auvergne, at Clermont, the Gallo-Roman poet and diplomat Sidonius Apollinaris, bishop of Clermont, realized that the local "fall of Rome" came in 475, with the fall of the city to the Visigoth Euric. In the north of Gaul, a Roman kingdom existed for some years and the Franks had their links to the Roman administration and military as well. In Hispania the last Arian Visigothic king Liuvigild considered himself the heir of Rome. Hispania Baetica was still essentially Roman when the Moors came in 711, but in the northwest, the invasion of the Suevi broke the last frail links with Roman culture in 409. In Aquitania and Provence, cities like Arles were not abandoned, but Roman culture in Britain collapsed in waves of violence after the last legions evacuated: the final legionary probably left Britain in 409.
But I think the collapse of perhaps more civilisations takes place over several generations and the fact of the collapse is probably not even apparent at the time. Rome and Greece are good examples. Successor civilisations usually adopt a considerable amount of cultural, political and social customs from the previous one. In other words, the collapse of a civilisation is often no bad thing for those involved.
There's also an issue of definition - its very difficult to say where one 'civilisation' ends and another begins there is arguably continuity between our 'civilisation' and Rome, which itself can be traced to Greek/Etruscan civilisation and so on.
I think the kind of collapse by resource exhaustion as envisioned by the likes of the Limits to Growth would be more similar to 14th century Europe than to the fall of the Roman Empire. "It's the statue, man, The Statue."
The move from centralised affluence to fragmented stockades housing war bands and king-lings happened within a single lifetime, and was very hard to miss.
The closest modern equivalent would be post-Soviet Russia, with the war-bands replaced by local mafiosos. Russia had some reslience because there was something of a tradition of self-reliance and barter before everyone's pay dried up. But what happened in Russia was hardly pretty.
A similar change in the West would be much more catastrophic, because hardly anyone has similar experience of self-sufficiency, population densities are often much higher - especiallly in the UK - and most people would be in shock if they could no longer buy essentials from supermarkets.
As for comparing a putative future collapse of The West™ to that of the Soviet Union, there's this lecture by Dmitry Orlov (I think I first got a link to that from ET, but I don't know in what thread). "It's the statue, man, The Statue."
If you were a merchant or someone else in the middle classes, I'd expect that it was very catastrophic indeed. If you were one of the peasants, possibly not so much.
The ruling elites were either slaughtered or adapted to new masters - which would doubtless have been catastrophic for them too.
We are schooled to think the Fall of Rome was a Bad Thing. Un-privileging the Roman POV allows for a broader, better, analysis.
The consequences of the Fall depend on when you date it.
shrug
Pays your money and takes your choice.
As for post-collapse period of our civilisation, I put up a scenario in a parallel diary.
The Antikythera Mechanism...
it is the common conceit of empires, as of adolescents, that all their elders are idiots and nothing worthwhile was ever invented or thought of until they came along :-)
the book Ancient Inventions iirc contains a very applicable quote in the Introduction... I'll see if I can find it later. The difference between theory and practise in practise ...