Yes it is, it's called an ectopic pregnancy, and if you suspect this has happened you should seek medical advice as soon as possible, it will be very painful if this has happened and can be dangerous.
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Yes it is possible, and quite common, for a fertilized egg not to attach. This is how some (but not all) Birth Control pills work.
You will have a early miscarriage and might not even notice it. It´s not dangerous.