As soon as a user joins a group, their Pick Set status within that group will be set to Active and will remain that way as long as the user is making correct picks from week to week.
Once a user reaches the group's "Strikes" (i.e., misses) limit -- either via picking incorrectly or failing to make a pick -- the status will change from Active to Eliminated.
While still considered to be a member of the group they joined, a user who has been Eliminated will no longer be able to make picks within that group.