Miners will still do the job and they will now mine to confirm transactions and they'll earn through the tx fees. Read these articles for better understanding.
[1]Will miners continue to mine bitcoin after that? [2]Will mining still be profitable? [3]Will miners used in mining evolve to consume less electricity and make mining profitable with fees in the future? [4]How will miners survive with tx fees? I doubt miners will still do the job if these questions are still questioned 50 years from now. I also think that instead of earning through tx fees alone, there would be methods invented to make mining profitable again before all bitcoins are mined in 2140.
[1] Yes
[2] Yes
[3] We don't know what the future lies ahead.
[4] They are already surviving today so by that time they can still but we don't have to think about it anyway, it's a century before it happens.
@batang_bitcoin: Thanks for the link
You're welcome.