Well, you'd better hope it's very stable.
The neck shift issue is actually pretty common with 90's Jag-Stangs, mine even has it. I have mine shimmed with a Fender-heavy pick.
The first part of the issue was a design flaw I've seen with 1st run Jag-Stangs where they cut the neck-slot a little off center, you can tell because the D and G strings don't follow the outside of the position markers on the fretboard in a straight line. Mine had this issue. That's part of why I shimmed the neck.
The other part of the issue is Pre-Dyna Gakki Jag-Stangs (Pre-1998, maybe even post 90 until the 2nd run so maybe some Dyna Gakki instruments, CIJ to be precise, are also affected). The problem with basswood as a body wood is it is very soft and the Jag-Stang's neck joint is a bit light on the bass side for the neck to rest against.
I just kept shimming my neck until I got it perfectly straight and it stopped, the wood just compressed till it would not compress anymore and it's been that way since the mid 2000's. Been a rock solid guitar despite that the whole time.
