Do negative assertions require proof?

A negative proposition is a proposition which asserts what something is not. A negative claimant is someone who makes a negative proposition. The "burden of proof" is commonly said to be owed by the maker of a positive proposition. Since they are asserting something which is not certain, one can only believe such a thing if an argument is provided, for that thing. Whereas, the burdeon of proof is often taken to not be necessary, for negative claims which are the default and opposite of an unjustified positive one. For example, a person claiming, "God exists" has a burden of proof, and a person claiming, "God does not exist", does not. This implies that belief in God is less of a default than absence of belief in God. God's existence would require justification; in its absence, we would by default assume the negative (or the "null hypothesis", that there is nothing to believe). However, this notion may be paradoxical, because it depends on how you designate what is or is not a "positive claim". For example, if I assert, "Object A does not exist", then while according to the above definition this would be a negative claim, this assertion actually does contain a positive claim; it implies, namely, "There exists at least one universe, in which Object A does not exist." Since the latter claim is a positive assertion, then the burden of proof follows: we must prove the existence of such a supposed world, or otherwise, assume the claim as void. All claims of nonexistence can be reformulated into claims of existence, using the trick, "There exists at least one universe in which [negative claim]." What does this tell us about the idea of a "burden of proof"?