When I used to use silk lines the way to treat a silk line that had gone sticky was to use Terabine.

Terabine is a solution that is used to speed up the drying/hardening of linseed oil, sprit based paints and vanishes. Terabine can bring a sticky line back to usable condition without all the bother of stripping off the coating.

Ideally the line was stretched out straight and then soak a soft cloth in terabine and rub it into the line. Leave to dry till the line has lost its stickiness. If the line is still still slightly sticky repeat the process.

Once dry polish it off with a chamois leather and talcum powder* then finish it off with a good greasing of red tin Mucilin. Or not if you want a sinking line.

*Tournament casters of old such as Marvin Hedge used to polish their lines with graphite powder to make them very slick.