Answer
No, a mutation or defective gene could never fully disappear from the gene pool. A person with a homozygous defective gene could mate with a homozygous normal person, but the offspring would be heterozygous. This means that some of the offspring will still carry the defective gene.
Work Step by Step
Typically natural selection gets rid of defective genes because the defective gene demonstrates itself as a phenotype, making it visible. With the gene being visible, the defect is visible, and chances of reproduction drop. Because the offspring would be heterozygous the mutation would not be visible as a phenotype, meaning the offspring would carry the gene but it would not be physically visible. Without the defective gene being visible, it would not affect the offspring, meaning that natural selection would not take place and the heterozygous would carry on, until they eventually mated and passed the defective gene onto their offspring.
