What do firebugs do when they "connect" by their rear?
They mate!

These matings can be very long


  When copulating, firebugs (Pyrrhocoris apterus) form tandems for prolonged periods. Half of the copulations of marked individuals in the field lasted longer than 12 h, and some lasted up to 7 days. (Schöfl and Taborsky (2002))


The likely reason for such a long mating is for males to guard the female to prevent future matings and therefore to prevent sperm competition


  males prolong copulations as a form of ejaculate-guarding under high competition with other males. (Schöfl and Taborsky (2002))