If mining process is over (all miners shut down their minning rigs ASICs), hashrate ceases to exist (drop to 0), the network is dead. No confirmation will be made by any miner as consequence of a dead network.

Do you really think there will be no single Bitcoin miner on Earth?

Because if there is only one miner left, network difficulty will be adjusted after each 2,016 blocks that takes about 14 days (2 weeks), after many times, difficulty will be re-targeted to be lower and lower. Chance to see all miners shut down their rigs at the same time is very impossible.

Bitcoin mining difficulty. Everything you need to know

With a dead network, you can not talk about its security. Dead is the end of everything.