The concept of rearward firing missiles was seriously considered for the V force circa 1970.
The very astute chief designer at Hatfield (guided weapons) - Polish origin, identified the need to throw a relatively small device out of the back of an aircraft, with lateral - vertical manoeuvre capability, and let the opposition run into it.
The counter argument was that ground based defences and planned air to air weapons would have an all aspect capability and much greater range; thus the task was to design a very agile, all aspect self defence missile.
The technical complexities and projected cost, precluded full development because more conventional defences, jamming and IR decoys were more practical and cheaper - forward firing chaff.
Aspects of that programme were know as ‘Taildog’, but this title was used - misused in other contexts.