A bit more on Thomasson
She's closest to van Inwagen. In Ch. 6 she addresses the matter of fictional people as opposed to characters, and she appeals to a story operator to deal with those. So her view has the same severe limitation as van Inwagen's, viz., what about all the nonexistent possibles that aren't mentioned in any story? (And as always, what's going to be the semantics of the story operator itself? She too might do better to shift to a pretense theory here.)
Judging by his remarks on referring to fictional characters, van Inwagen would take the Conservative line on essences for fictional people. But Thomasson makes McMichael's point (without citing McMichael) about fictional people having everyday modal properties, which seems to refute the Conservative line. So perhaps she is a Lycanian Haecceitist, but she doesn'tt pursue the matter.
Negative existentials: Here too she follows van Inwagen. "Lear never existed" means only, there never was any such person as Lear. But as in van Inwagen's case, "Lear" there has to name the character, not the person, and what does it mean to say that there never was any such person as that character (an abstract object)? Presumably that there never was any person corresponding to the character. If one takes the Conservative line, that will work; it's roughly Russell's pretty good solution to the problem of negative existentials. (The Conservative line is bifurcative vis-a-vis the description theory of proper names.) But Thomasson doesn't, or can't, take the Conservative line. What should she say instead? Probably that there never was any person who had all or most of the properties Ascribed to Lear in the play. But that won't work so well, because of the Kripkean possibility that unbeknownst to us there actually was someone who had all or most of the Lear properties. Oh, well, no one has an acceptable theory of negative existentials.
It's worth asking what kind of abstract entity a Thomasson character is. She says little about this, seeming to regard fictional characters as sui generis. If she does go Haecceitist, though, she can say that a character is just a "blank" haecceity (cf. the fourth objection to unexemplified haecceities) individuated by the circumstances of the character's creation.
Incidentally, her own view of character individuation, which is like mine but not as strict, affords a ground for resisting her view that characters can cease to exist. (Though I have no dog in that particular fight, I am uneasy about the idea that characters can cease to exist, at least as easily as she says.) If we admit that characters are created, she says, symmetry suggests that they can also be destroyed, and only a lingering Platonism suggests otherwise. But we have a reason to reject the appeal to symmetry: haecceities or not, characters are identified and individuated by the circumstances of their creation. They are not identified and individuated by anything to do with what happens to them later. So a temporal asymmetry is built into their nature.