Jones was a second-in-command Agent, and bent on catching Neo and winning the war.
The Matrix Reloaded
In the second film he was about to intercept Neo when he was turned into a Smith who had currently left the agents in a new idea of taking over the MATRIX.
Although Smith did copy over the Bluepill that Thompson had taken over, he did not actually copy over Thompson's own code, as he is seen later on chasing Trinity and the Keymaker. However Agent Jones was completely destroyed and in the end as he was never uploaded after the war of Zion.