Given e.g. one lost the private key to a specific bitcoin address, is there any way to make sure no more bitcoins can be transferred to it since it effectively became a bitcoin-furnace?
Unfortunately, there is no way to do any such thing. Your only option is to manually inform any business partners that the address has fallen out of use.
As the only way to proof indubitably that you were the owner of said address would be to sign a message with the respective private key, I don't see how anyone could justifiably shut down an address.