If mining of new bitcoin will stop tomorrow there will be an apocalyptic scene to the bitcoin protocol, there will be only unconfirmed transaction
The old Bitcoin Core clients (up to v0.3 or v0.4, I think), had a built in CPU miner. I think we should re-enable it!
For CPU mining, this would not make sense. The current difficulty is so high that it would take a good two years (at least)in order for the difficulty to return to a level that is profitable for CPU mining.
If for example the difficulty were to decrease by 50% then it would need to take an extra two weeks to find 2016 blocks (this can happen either over one difficulty period or over several, however it needs to take a total of an extra two weeks). In order for the difficulty to decline by 75% (or decline a further 50% after declining 50%) i would need to take an additional 2 weeks to find an additional 2016 blocks (or a total of 4 weeks). This does not sound like a lot of time, but you need to take into consideration the fact that CPU mining is really only profitable when difficulty is in the 1,000's but right now the difficulty is just shy of 36 billion.
This means that it would need to take an extra 22 times two weeks in order for the difficulty to get to ~8500, which is still in the upper range of what would be profitable for CPU mining