Basically, Bitcoin block could have gone empty. Can someone remind what happens when almost empty blocks are mined in a row for, for example, 1 hour?
There's no such thing as empty blocks as a block must at least have the mandatory coinbase transaction. One (coinbase) transaction could be considered "empty", it depends on your definition of an empty block.
Nothing happens even if the miners would mine dozens of almost empty blocks. I would only raise the question why there are so few transactions. Everybody on vacation or on heavy party hangover? Internet broken?

I remember that some people said, empty blocks are bad for the network security.
What could possibly be the explanation for such a claim? Little to no transactions to mine into blocks would be seriously concerning. But that's basically all I can think of (I don't know all, for sure).