[First year university archeology] Is it possible to devise a breeding plan that will result in a recessive allele becoming universal among each generation in a population?

Imagine that you are breeding a specific type of plant or animal and there is a characteristic that you want your breed to have, but it is a recessive one. Is it possible to devise a breeding plan that will result in that characteristic becoming universal among each subsequent generation?

I know that recessive alleles must be present on both chromosomes to be expressed. But is it possible to someone breed a plant or an animal to be homozygous for something?