Well... I spot an error in the quora answer straight away...
If all miners would turn off their mining equipment, difficulty wouldn't just magically drop. There's a diff retarget every 2016 blocks, and even then the amount the difficulty can increase/decrease is limited (my memory is fuzzy on how much it can rise/drop... You can look it up on github, on the repo of the reference client it's hardcoded... I even posted the exact line in the code somewhere in the past, but i'm to lazy to look it up).
So, if everybody would turn off their mining equipent and there wasn't a hard fork to solve the issue, difficulty would stay exactly as high as it currently is forever. People could still broadcast transactions that would reside in the mempools of the nodes for some time, but no transaction would ever be included in a block (so no confirmations, and as soon as an unconfirmed tx is purged from most mempools, it's like it never existed in the first place).
As for the rest of your question: this has been discussed at lenght so many times before... Just search the forum for questions like "what happens if 21 bitcoins are mined".
TL;DR; the most common answer is that miners should have enough incentive to continue mining because of the mining fees... I'm not sure if that will happen, but i probably won't be around anymore by that time either, so i'll never know if this is/was a correct statement anyways
. Maybe we'll have switched to a different algo by then, maybe miners will have enough incentive from the fees alone, maybe people will mine altruisticly, maybe companies using bitcoin will continue mining so their business model is sustainable, maybe bitcoin died long before this point was reached,....
