Explainable anomaly detection
The LIME framework can probably be used to do this as well.

Outlier detection sets a specific label to outliers (say 1), and another one to inliers (say 0). From then on, you can train interpretable models (decision trees for instance) to predict the labels set by your unsupervised model.

I don't know much about SHAP values, but I guess, with this approach, you could do the same.