Because the centromere is the point of attachment for the mitotic apparatus, acentric fragments are not evenly distributed to the daughter cells in cell division (mitosis and meiosis). As a result one of the daughters will lack the acentric fragment.
Lack of the acentric fragment in one of the daughter cells may have deleterious consequences, depending on the function of the DNA in this region of the chromosome. In the case of a haploid organism or a gamete, it will be fatal if essential DNA is contained in that DNA segment. In the case of a diploid organism, the daughter cell lacking the acetric fragment will show expression of any recessive genes found in the homologous chromosome. Developmental geneticists look to cells and cell lineages lacking unpaired chromosome segments produced this way as a means of identifying essential genes for specific functions.
Acentric fragments are commonly generated by chromosome-breaking events, such as irradiation. Acentric fragments can also be produced when an inverted segment is present in one member of a chromosome pair. In that case, a crossover event will result in one chromosome with two centromeres and an acentric fragment. The acentric fragment will be lost as explained above, and chromosomes with two centromeres will break unevenly during mitosis, resulting in one daughter lacking essential genes. 
- Acentric Fragment, In: Sydney Brenner and Jeffrey H. Miller, Editor(s)-in-Chief, Encyclopedia of Genetics, Academic Press, New York, 2001, Page 2, ISBN 978-0-12-227080-2, 10.1006/rwgn.2001.1750.
- Introduction to Genetic Analysis (Looseleaf). Macmillan. 2008. ISBN 978-1-4292-3323-1.Google Book Preview