Fuzzing is a common technique to detect faults.

In the case of REST APIs, common types of faults are HTTP 500 server error responses, and mismatches with what declared in the OpenAPI specifications.

However, there are several types of security properties that can be automatically checked as well, even when there is no formal specification of the access policy of the API. For example, what if a PUT/PATCH is denied (403), but then a DELETE is accepted (2xx)?

The linked article on arXiv shows a series of experiments on more than 50 APIs using 9 different kinds of security "oracle" checks. Those are implemented in the open-source fuzzer EvoMaster.