Dependency syntax has long been recognized as a crucial source of features for relation extraction. Previous work considers 1-best trees produced by a parser during preprocessing. However, error propagation from the out-of-domain parser may impact the relation extraction performance. We propose to leverage full dependency forests for this task, where a full dependency forest encodes all possible trees. Such representations of full dependency forests provide a differentiable connection between a parser and a relation extraction model, and thus we are also able to study adjusting the parser parameters based on end-task loss. Experiments on three datasets show that full dependency forests and parser adjustment give significant improvements over carefully designed baselines, showing state-of-the-art or competitive performances on biomedical or newswire benchmarks.