This question is suprisingly hard to answer thoroughly. Even though the conenctration camps were somewhat centralised and lead similarily across all camps (there were around 1000) there were huge differences. You had the extermination camps like Auschwitz-Birkenau or Treblinka, where thee majority of inmates were killed immediatly on arrival, and you had the other camps where the concept of "Extermiation through work" was used, where inmates could survive much longer. And you had camps where political prisoners were held, some of which survived for years and years.

Most inmates who survived for a substantial amount of time made themselves "important" in the camp. Some were so called "Capos", inmates who served as kind of a gaoler to maintain discipline between the inmates. A different but rather famous case is Josef Paczynski who survived Auschwitz for five years by becoming the personal hair dresser for Rudolf Heß, the commanding officer of the camp.

I couldn't find a definitive prove for who was the inmate who spend most time in a concentration camp, but Kurt Schuhmacher, an important politician for the Social Democrat Party of Germany was in a KZ for most of the time between 1933 and 1945, who only spend short time (between March 1943 and August 1944, and then again from September 1944 until the defeat of the German Reich) in partial freedom after being imprisoned in a KZ in July 1933, so he spend nearly 10 years (of 12 years of Nazi regime) in a concentration camp.