Blonde hair can be dyed brown with wonderful results if the dye job is done properly. Blondes who dye their hair brown should pay attention to the wording on the color they plan to use. Any mention of "red" or "warm" isn't appropriate for a blonde who wants to go brunette.
Going from blonde to brunette means changing more than just the color of the hair. Because makeup is dependent upon hair color and other factors, changing makeup colors will be necessary. It might also be necessary to change shampoos to help keep the dyed brown hair shiny and looking healthy.