According to Heliocentric, but also Neo-Tychonian theory, there should be no such thing as negative parallax.
If parallax is rightly called so, that is, if it is an optical illusion of apparent movement, due to Earth moving around the Sun, then it follows there can only be parallax in one direction at a time : Earth cannot make its orbit around the Sun by opposite ways at once. The parallax must then be what is usually called parallax, or positive parallax.
If a Heliocentric does hear about negative parallax, he writes it down as "bad measures". But if the measures for negative parallax are bad, so are those for positive parallax, they are measured by the same tools.
If the parallax for 63 Ophiuchi (or stars with greater negative parallax) is really a positive one, measured as a negative one, due to common parallax of surrounding stars hiding it, where is the limit where these show against background of non-parallactic stars or not visibly parallactic stars?
Or if it is a positive one, measured as a negative, due to common parallax of all stars, then one must add its value (inverted to positive) to a "non-parallactic" star and also to each positive parallax.
But that means about doubling the parallax of alpha Centauri, which in turn means it is about twice as close, 2 light years instead of 4 light years : rather it would be the common parallax of all stars which were 4 light years away and 63 Ophiuchi would be exceptionally distant. But that also ruins modern cosmology.
Same observation basically holds true in Neo-Tychonian system, where all stars are supposed to be moving with the Sun each year.
But if on the other hand parallax is a real proper movement, really inherent in the star and in each star, due to for example an angel moving it, then it is not parallax as usually understood, negative parallax is perfectly explicable, it is an indication angels are giving in obedience to God there was sth wrong with parallax theory in the first place. And if so, the phenomenon called parallax has nothing to do with parallax, is no indication of distance and stars can all be much closer than even 2 light years away.