Empirical studies send mixed messages as to the magnitude of social stigma associated with the take-up of social transfers and the impact of stigma on take-up. These mixed signals may be related to the fact that stigma and program participation are likely to be jointly determined. If there is a high (low) degree of participation in a program, stigma is likely to be lower (higher) due at least in part to that high (low) degree of participation. This is because the more eligible persons participate, the less one can single out specific individuals for stigma because they use the program. This note suggests this theoretically with a simple model showing that we may have in an idealized setting two equilibria: one with stigma and zero participation in a social program, and one with perfect participation and no stigma.