Pregnancy on birth control

Samantha
This is a complicated question.
Now, I know it's possible to get pregnant on birth control (if taken incorrectly) and I also know it's possible for sperm to survive in a woman's body long enough to impregnate an egg sometimes days later (heard and know several stories). 
However, is it a realisticly possible to get pregnant on your "off week" of the pill because the sperm has survived until then?
I take my pill on the dot and haven't missed any days, I'm NOT late on my 'period' right now and I know that technically you can have sex on your off week and still be protected but I'm curios. Sorry for the long question but I'd love to hear your thoughts!