Cleaned Coins

Totally depends on the coin and the price and rarity. There is no definitive percentage. A $2000 coin is probably not going to drop to $1000 because it comes back genuine. But a $40 ASE is definitely going to drop to spot value.

I'm not entirely sure if it's true but I have heard that for large cents there is almost an expectation that they may have been cleaned at some point and there isn't much impact to their value, at least for lower grades.

It does depend on the coin but the figure I once read was that numi coins lose about 70% of their value if they have been cleaned. From many coins that I collect (Australian pre decimals) that figure is about correct. I've seen coins that are similar to others (but cleaned) and the problem free coin makes $50,000 and the cleaned coin struggles to make $15,000.
For less rare coins I have seen many cleaned coins struggle to make 20-30 dollars when similar problem free coins are bid to over $100.
For conditional rarity coins the loss of value can be 90 to 99%. I have a coin where one side is pristine Gem and the other side had a light clean. If both sides were pristine it would be worth several thousand but the cleaning makes it not worth $50.