The case of having a chromosomal fragment joining to a nonhomologous chromosome is called translocation.
Children who have Down’s Syndrome will either have an extra chromosome 21, thus having a total of 47 chromosomes, or about 5% receive a combined 14-21 chromosome combination. (Chromosome 21 links to #14).
In meiosis, the combined 14-21 chromosome will actually behave as a single chromosome. Should this mutated gamete join a normal one during fertilization there will be three chromosome 21’s in the resulting zygote.