We've moved in twice.
First time, builders had left loads of dust and rubble and bits around the place, and the loo was unflushed (grim). And the bins had already arrived before builders finished so of course those were filled as well so we couldn't use them until after collection day.
Second time, we bought from someone who was moving abroad and didn't want to bring lots of big things so left broken fridge, battered cooker, few bits of furniture and a cupboard full of glasses amongst others (had wanted to sell us the white goods and curtains, we said no and to remove them...). And all the curtains so chock full of dust having not been used for about 3 years. But the bathroom "set" (pine towel holder, toilet roll holder, toothbrush holder etc) had "sentimental value" and she brought those with her, which we agreed, but she literally ripped them off the wall and left a number of fist-sized holes in the bathroom plasterboard behind the vinyl wallpaper. And no, she hadn't cleaned as she left.
So our experience has always been to deep clean on arrival and be armed with rubber gloves, rolls of bin bags and kitchen towels, cleaning sprays and bleach for that first day.
I've also been involved in moving an Uncle (who is a priest) on a number of occasions - the houses are always taken over from other priests and while 1 was a joy to behold (very active Parish Council!), most have needed a very good scrub too.
When we moved out, I just tried to make sure we had done a reasonable job of leaving it clean, bins emptied, no gunge in the sinks, floor swept (movers had thrown the hoover into the van hours before even though I had it safely in a cupboard!) - but I didn't get a chance to mop as we left (pouring rain day and estate agent problems both sides meant we were under pressure to get out and also fighting about getting new keys) which annoyed me. But we did leave all manuals, some spare "headed" notepaper with the address (which we had printed for personal thank you notes instead of cards after our wedding the year before) and a bundle of envelopes, spare keys labelled, good luck card and a bottle of wine. And the pots of paint for touching up different rooms were in the shed, labelled, as we'd had to paint the entire house ourselves, and a couple of spare tiles for the kitchen splashback.