If so, what were their motives and stories. How did DDR troops react?
First: I'm neither a Historian nor a scholar in this field, but please find the source for the following informations at the bottom of my post.
Germans living in the federal republic were pretty much free to choose wherever they wanted to live, so there was no need to "flee", but the state security of the GDR wasn't so happy about immigrants from the west. Immigrants arrived in prison-like camps and had to undergo very intensive background-checks, as the GDR feared them to be spies trying to infiltrate the east. The residents of the GDR supposedly frowned upon western immigrants and most of them were put under surveilance for years to come.
A statistic conducted by West Germany's border security agency in 1966 shows, that most people would emigrate because of personal (loved ones, family, etc) rather than political reasons.
Until 1961, about 20,000-50,000 germans would emigrate to the GDR every year - though this number significantly dropped after the wall was built.
Source: Bernd Ströver ( Professor of Modern History at University Potsdam) - Zuflucht DDR: Spione und andere Übersiedler; C.H.Beck 2009
Ps.: Prominent figures who emigrated from west to east would be Wolf Biermann (allthough he left before the wall was built), a famous artist / singer songwriter (who later was forced to leave the GDR again) and certain members of the terroristic union RAF like Inge Viett and Susanne Albrecht, who fled prison.
Also, please excuse any grammatical errors, as english isn't my first language.
Edit: You can read about Wolf Biermann's story here