When I write a polygon geometry whose western edge is equivalent to -180.0, but in Spherical Mercator (-20037508.342789244), the longitude value switches signs and becomes positive. I have tried the same process, but writing to a GeoJSON file and no problem occurs.

Is there any value modification occurring when features are written to the Spatialite format?

I can provide a very simple workspace to replicate this if it is needed.

For what it's worth, I believe this is a precision problem.

Simply
changing the western longitude from -20037508.342789244 to
-20037508.34278924 "solves" the problem. It does however translate to
changing the actually geometry because something that originally was
equivalent to -180.0 is now -179.99999999999997.