If the same custom field name is used in several projects for a custom field and custom fields are distinct (e.g. projects do not share fields configuration), issue search produces incorrect results for the following request:

"custom field" is EMPTY

Namely, issues with non-empty values for "custom field" are returned as well.

The following requests

cf[10201] is EMPTY
or
"custom field" is EMPTY AND Project="prj"

does not work as well (include issues with non-empty custom field values).

The only way to workaround is to use the following jql:

cf[10201] is EMPTY AND Project="prj"

This is definitely a bug and should be fixed.