At the conclusion of the Green Lantern: Rebirth mini-series, the Parallax entity is imprisoned in the Central Power Battery on Oa once again. It is next seen in the Sinestro Corps Special, where it possesses Kyle Rayner. But, how did it get out? We clearly see that Superboy-Prime and Cyborg Superman are busted out of the sciencells on Oa in the same issue, but there's no mention of how or when Parallax escaped.
The answer is: Krona. The Malthusian who tried to look at the beginning of the Universe with a "time viewer", and caused both the aging of the Universe, evil to spread throughout the Universe, and the birth of the Guardians of the Universe.
It was Krona, who returned after the JLA/Marvel crossover, and began secretly collecting all the Emotional Entities in order to gain absolute power over the Universe. (I believe this happened somewhere around GLC.v4.#035, June, 2009).
It was after Sinestro's Corps was fully started that Parallax was put into Kyle Rayner. It was Sinestro's Corps (possibly with Krona, or the Anti-Monitor) who freed Superboy Prime and Hank Henshaw the Cyborg Superman from Oa.
When Krona was ready (GL.v.4#53, June, 2010), he took the Ion Entity out of Sodam Yat, who was changing his home star from red to yellow, giving all Daxamites superpowers, and brought Ion to Ryut, Atrocius' homeworld (GL.v.4#54). Krona started to collect all the Emotional Entities as they appeared (GL.v.4#62, Mar2011), until he took them to Oa and infected the last Guardians of the Universe with them. Parallax was put into the Green Central Power Battery to possess the Green Lantern Corps (except those who had previously fought against Parallax) (GL.v.4#64, May, 2011).
The Emotional Entities left Oa after Hal Jordan killed Krona and the Guardians of the Universe reestablished control over the Green Lantern Corps (GL.v.4#67, Aug, 2011) The next story arc with the Emotional Entities was Relic.