Then miners will stop mining because they wont get any Bitcoins lmao 
There will be no block reward in 2140. It could be early than 2140, may be 2100 as the difficulty increases all the time. However, if bitcoin still exists then, there will be transaction fees. Miners will live on transaction fee. The transaction fee will be high enough to support the miners.
transaction fees should be high enough to support miners. looks like around 2032 block reward will be .78btc. that's just around the corner. by 2050 block reward will be .0488 btc....its then another 90 years to 2140. so yeah transaction fees will support network....for bulk of its existance