If this would happen on a truly large scale, like covering 60-80% of the population, then it would probably cause a small temporary downside movement, because it would be a negative event - someone sending people empty wallets, hoping that they would use them and steal their coins/
This is what exactly I'm thinking if there's a newbie who has received the empty Bitcoin paper wallet and due to curiosity, a newbie will use it to receive the Bitcoin purchase(
or come from somewhere else) even it's a small amount it can be touched the demand and supply principles where Bitcoin price determines the value.
It sounds like a trap to all naive newbies who didn't have knowledge about Bitcoin and they become a victim of fraudulent but if the old member received it, for sure they will check first and ignore it, how can you put your valuable crypto assets if you don't have a key (
which is always remembered the golden rule ''not your key, not your coin'')
At this point, the Bitcoin price will surely move the price and I think that's not big enough to shake the entire market not unless if every wallet will receive 5 Bitcoin.