In the Terminator Franchise, John Connor has to send Kyle Reese back in time to 1984 to protect his mom from?

the T-800 terminator. If Kyle Reese failed to protect her and John Connor was never born in the 1984 Kyle Reese was sent to then what would happen to the John Connor that sent him back from 2029? Would he just disappear and the time line reset itself? How would this twist on events appear to the people from Kyle Reese's 2029 if Sarah Connor died/John Connor was never conceived.?