Archiving takes a client off your active roster without deleting anything. Their program, logs and history all survive, and unarchiving puts them back.
On the free plan there is a condition attached, and it is the single most important thing on this page.
The 14-day wait on Foundation
Basecamp warns you before you do it: on the Foundation plan, a 14-day wait applies after archiving before you can unarchive that client.
So on a free plan, archiving is not the casual, reversible tidy-up it is elsewhere. Archive somebody on Monday, change your mind on Tuesday, and you are waiting until two weeks have passed. The archived clients screen counts it down for you: it tells you when you can unarchive them, in days, hours or minutes.
This matters most in exactly the situation where you are most tempted to archive: you are at the Foundation limit of 3 clients and somebody new wants to start. Archiving an existing client to make room means that if the new arrangement falls through, you cannot immediately restore the person you moved out of the way.
Do not shuffle people in and out of the free plan's three slots. Upgrade, or wait until somebody genuinely finishes.
Archiving somebody
From the client in the sidebar. Read the note if you are on Foundation. It is there specifically so the wait is not a surprise. If it fails you are told plainly and can try again.
Bringing somebody back
Archived clients has its own heading in the sidebar, and Show archived reveals them alongside your active list when you want to see everyone at once. Hide archived puts them away again.
Unarchiving asks you to confirm, then runs a short countdown before it commits. The prompt tells you the client will return to your active clients. It is a deliberate pause rather than a delay for its own sake.
What the client sees
Archiving is not invisible to them. If they use Workout Titan Nutrition, their app tells them their coaching account is archived and stops sharing nutrition data with you until you restore access.
Tell people before you do it. Somebody discovering it from an app notice, with no message from their coach, will reasonably assume they have been dropped.