My question is: Is it possible to stop the block generation when mempool is empty?
Impossible, miner will just mine empty block (block which only contain coinbase transaction). Here are few example (each from different pool),
My assumption is that he is talking about a side chain with no subsidy, therefore there is little incentive to mine empty blocks.
In that case, security is still an incentive, unless it is an entirely closed and centralized system (in which case there is no need for a blockchain at all).
If block mining stops, then an attacker has as much time as he likes to mine an alternative chain that is longer than the current chain. As such, he could remove confirmations from transactions or replace transactions entirely.