The -e flag changes the handling of erroneous packages, those that cannot be found or are malformed. By default, the list command prints an error to standard error for each erroneous package and omits the packages from consideration during the usual printing. With the -e flag, the list command never prints errors to standard error and instead processes the erroneous packages with the usual printing. Erroneous packages will have a non-empty ImportPath and a non-nil Error field; other information may or may not be missing (zeroed).
However, at least some compiler errors still end up getting written to stderr. For example, go list -e -export -json -gcflags=-bogus math >/dev/null shows output for me.