Someday all Bitcoins will have been mined.
Is mining then still necessary ?
And is the 51% problem still in existance ?
Actually, it is easiest to 51% attack after all bitcoins have been mined due to the decrease in difficulty...
Difficulty may not decrease since no new coins are released to the trading market. There would be much more demands. Miners can still earn from transaction fees which is probably around $10-100. I don't think much people would stop mining since even advanced ASICs would have came out. If everyone stops mining, many would turn on their machine again to profit pushing the difficulty up.