In this paper, we explore conjunctive query rewriting, focusing on queries containing universally quantified negation within the framework of disjunctive existential rules. We address the undecidability of the existence of a finite and complete UCQ-rewriting and the identification of finite unification sets (fus) of rules. We introduce new rule classes, connected linear rules and connected domain restricted rules, that exhibit the fus property for existential rules. Additionally, we propose disconnected disjunction for disjunctive existential rules to achieve the fus property when we extend the introduced rule fragments to disjunctive existential rules. We present ECOMPLETO, a system for efficient query rewriting with disjunctive existential rules, capable of handling UCQs with universally quantified negation. Our experiments demonstrate ECOMPLETO's consistent ability to produce finite UCQ-rewritings and describe the performance on different ontologies and queries.