Impossible, if everyone has a job what happens to the people working at the unemployment office
It's actually sad, but the "unemployment market" is so big in Belgium that it's all but sure that they are not doing their job well...in order to keep their job, if you see what I mean.
Still missing the point.
Employment is a contract between employer and employee. You, as employee, contribute labor and knowledge to an undertaking of your employer. You perform specific duties which are part of a JOB.
That's not the same as growing your own food to live and hunting a buffalo. You are not "employed" by anyone to do that. You just have to do it.
How this is not common knowledge is mind-boggling.
Anyway to answer the question, no. "Full employment" actually usually means a 3-4 % unemployment ratio I think (it was called "residual" unemployment when I studied, in french), due to youngsters ending school and transitionning to the labor market, people looking for better opportunities, people from an old kind of industry (coal, for example) who have to adapt to the newer ones, people pursuing another interest at that precise moment, people being laid off by struggling companies etc. It wouldn't even necessarily be good for the economy, if there are too few available employees, wages will go up which can lead to inflation. Capitalism needs a "buffer".