How it is possible that blood group shows that a person is not the son or daughter of their parents?
Each person has two alleles for the blood type. The two A and B alleles are dominant. So, you don't need A/A to end up with blood type A, it could also be A/O. Having both A and B results in blood type AB. Having none of these, results in blood type O.

Following these rules, from parents being AB and B (genetically either B/B or B/O) you would expect these possible blood types for their children:
- A/B
- A/O
- B/B
- B/O

The Rh factor (positive or negative) is inherited similarly. The positive allele is dominant, so genetically +/+ or +/- would be positive, only -/- is negative.

There is a rare case of a "cis AB" mutation, where the A and B antigens are in just one allele (wiki, paper). Then the genetic alleles of an AB type could be AB (in one allele) and O.
The children of the couple could then be
- AB/B
- AB/O
- B/O
- O/O

So, there would be two possibilities for the case you describe.


The parents are not the biological parents of the child.
The mother is cisAB/O +/- and the father B/O -/-


edit: or a third way would be of course some de novo mutation in the child, resulting in the loss of A/B from the mother

edit2: maybe to answer your actual question "How can a child not be the child of its parents?".. adoption, in-vitro fertilization with donated eggs and/or sperm from other people, mix-up in the hospital..