did you check the burette calculation ( if it marks 50 to1 ) like an upside down numbering so that in each case when you minus values initial to the final reading then each reading you got in minus values? then for the final calculation, you may get your result.
If you mean the results were actually below zero, then this is most likely because the incubations were not done in complete dark. If some light was present, photosynthesis can produce oxygen, leading to a negative BOD. Hope this is helpful!
If BOD measurement has been done through respirometry and by BOD you mean (BOD of sample+nutrient+seed)-(BOD of nutrient+seed); the negative result means the microorganism culture is not acclimated to some compounds in your sample, and those compounds are toxic/inhibitor for microorganisms activities.