After a foaf:Person is no longer involved with a foaf:currentProject, or has been inactive for some time, a foaf:pastProject relationship can be used. This indicates that the foaf:Person was involved with the described project at one point.

If the foaf:Person has stopped working on a project because it has been completed (successfully or otherwise), foaf:pastProject is applicable. In general, foaf:currentProject is used to indicate someone's current efforts (and implied interests, concerns etc.), while foaf:pastProject describes what they've previously been doing.