It would depend I guess on the dye being used. Many dyes will give degradation products which are separable using HPLC. Sometimes the degradation products might overlap in HPLC. In some cases hydrolysis of the degradation products can make them separable. Once you have a means to a) identify and b) quantify these degradation products, you can follow a standardized viability test e.g. cell counting kit (CCK-8) or PicoGreen DNA quantification.
Perhaps using a few cell lines would be a good approach and concentrations similar to those used in staining protocols. You could play around with a variety of degradation scenarios which can closely mimic staining protocols or long term storage, etc.