Feed importer: field collection processor settings
Finally got it to work!

Settings for Field collection processor

Do not update existing field collection item

Field name: (The machine-readable name of the field collection)

Host entity type: Profile

Is field: unchecked (FALSE)

Field/property name of Host entity GUID: pid

Identifier field name: pid

Mapping for Field collection processor

pid => Host Entity GUID

(and my other fields of course)

Note:

pid is the Profile ID.