Based on the community answer, you generally do not need to reapply a traditional C-41 stabilizer after cleaning. Older color negative films were treated in processing with a mild formaldehyde-based stabilizer that helped harden the emulsion and act as a biocide; later processes used less hazardous biocides instead.

The practical advice given is that if you want to inhibit further mold growth, a mild water-based biocide can be used rather than trying to recreate the original stabilizer step. One suggestion was a heavily diluted over-the-counter antiseptic solution. The key point is that the film’s gelatin layer can support mold, so stopping biological growth matters more here than restoring the original chemistry.

If mold has already attacked the emulsion, some damage may be permanent. The safest course is to clean carefully, then digitize the negatives as soon as possible and repair remaining defects digitally if needed.