Liquids cool down during evaporation when the particles with higher energy escape from the liquid. Because of this, the liquid left behind has less energy than it did before evaporation occurred. Therefore, the temperature of the liquid is lower.
Evaporation does not stop suddenly when the highest energy particles break away from a liquid. In a liquid, particles are moving at different speeds, and they interact. This interaction causes some to slow down and others to go faster. After evaporation begins, the total amount of energy in the liquid is lower, but some of the particles that speed up are able to free themselves. Therefore, evaporation continues.