My initial interpretation is that social debt is the antithesis of social capital and represents things like burning one's credibility, demonstrating untrustworthiness, losing respect, etc.

Some querying on the Internet shows people discussing social debt as a software engineering concept. In that context, it seems to be parallel to the idea of technical debt but revolves around the quality of the social dynamics of a team rather than the quality of the code.

In any case, it's definitionally not objectively measurable (and I'm not sure why that would be desirable), since it's about people's perceptions and subjective experiences with each other. One can, of course, subjectively measure it.