What happens if I step off the back end of the strip, and does my foot have to touch the floor behind the line?
If both of your feet go completely behind the end line, the referee halts the bout and gives a touch against you. One foot behind the line is fine, and so is a heel hanging over the edge, because any part of a foot on the line counts as on the strip. Your foot does not have to touch the floor behind the line, either. Think of the end line as a wall that rises straight up: once both feet are entirely past that wall, even if one is in the air, you are off.
The strip is built to give you room. It is 14 m long, and each touch starts with your front foot just behind your on-guard line, 2 m from the center, so you have about 5 m to retreat before you run out of space. The last 2 m before each end line is marked in a different color so you can feel and see where you are without looking down. There is no warning call from the referee, so that colored zone is your only reminder. After every touch you both go back to the on-guard lines and the space resets.
A few related rules are worth knowing. If you are pushed off by accident, for example in a collision, there is no penalty. The sides work differently: one foot completely off the side stops the bout and you restart a meter back from where you went off, which can push you over the end line and cost you a touch that way. Going off the side with both feet means anything you did after crossing is annulled. And when the referee resets you after an ordinary halt, you are never placed behind the end line if you were in front of it.
If you keep losing touches at the end, the fix is awareness and footwork. Learn to feel the color change under your back foot and treat it as the signal to stop retreating in a straight line. From there, hold your ground with a parry, a counterattack or a step forward to win back space, because an opponent who has pushed you there is about to finish. A good drill is to fence short bouts that start with your back foot already in the end zone, so you practice getting out of trouble instead of backing into it.