IIUC, the tailess configuration was intended to prevent the trans-sonic shockwave generated by the main wing from interacting with horizontal tail surfaces in a detrimental manner. In theory the wing generated shock waves could blank the horizontal surfaces and make them ineffective and/or cause buffeting and destructive harmonics - making it difficult or impossible to pull out of a dive and/or causing the loss of the tail surfaces. Apparently it did not work as desired - primarily due to controlibility issues.
However, in answer to your original question, I present the F9F Cougar - an airframe that used some of the information gained from the X-4 program.