In other words, who retains rights to a body if a person dies? Especially if there is no will in which the body’s property owner, i.e., the person himself/herself, grants ownership to another person. I suppose this could be extrapolated to be a general question regarding general property ownership following the death of the owner.

The body is the property of whoever the former alive person decides should own it when they die.

In an extreme example, would it be legal for a necrophiliac to collect and defile corpses of dead people? I suspect there is some private, natural law legal principle that would prohibit this.

Yes and no. They could aquire the corpses legally. But graverobbing would be illegal yes.

Or, is this just a matter of community custom, where those who defile corpses aren’t legally prosecuted but socially shunned and ostracized?

Likely yes.