**** Not a teacher ****
I think here it means "to leave for a particular purpose" (in this case to cohabitate), but I am not sure.
I got this from here. The example sentences given in that online dictionary are:
But in the example it has "go off to" and in your sentence it says "go off and". So please wait for confirmation from a teacher or senior member of this forum if this meaning is correct.
Student or Learner