jq -e always exits with status 0 when passed empty input. For example:

$ echo | jq --exit-status 'false'; echo $?
0

Consider a use case like this one:

call-some-json-api |
jq --exit-status '.field == "some-value"' &&
take-action

If the API call fails and output is only written to stderr, take-action will still run as though the call succeeded, and "some-value" had been set.

This may be related to issue #667, but that one has been fixed on master, and this bug is still present.