What type of alleles can shorten the life span of an organism?

No, that doesn't occur naturally. However, the word you're looking for are deleterious alleles. Over time, natural selection weeds deleterious alleles out of a population — when the dominant deleterious alleles are expressed, they lower the carrier's fitness, and fewer copies wind up in the next generation. But recessive deleterious alleles are "hidden" from natural selection by their dominant non-deleterious counterparts. An individual carrying a single recessive deleterious allele will be healthy and can easily pass the deleterious allele into the next generation.