Well, they get on the back section of the train, which then accelerates to warp factor eight and catches up with the front train, then reattaches. Simple 
A unescapable principle of train timetabling is that all trains need to be back at their starting point at some time to do it all over again. The same applies in general to commuting passengers.
The OPs idea would result in a pile up of trains and passengers at Göttingen, unless the same train going back to Hamburg stops to reattach trains. In which case you lose all the time you saved on the out journey in the process of recoupling on the return journey.
It would make sense, however, if there was a way of recoupling trains on the move. Or if Göttingen train returned to Hamburg under its own steam. But in both these scenarios both sections of the train would require engines, so why bother having them as a single train to begin with?