> If they want to just shut the whole thing down, that is fine too.

Actually if it's under a non-restrictive open source licence, it's not fine at all - the code will still be legally available for everyone.

I should've worded that better. Of course they can't pull the existing versions, but then can shut down any further development and support.

> but then can shut down any further development and support.

Not really. A fork can easily continue developing and supporting it.

The original copyright holder can require the fork be distinguishable and non-confusable with the original project. There is plenty of precedent in that respect.

There isn't much that can be done with lax distribution licenses, but there is still much that can be done under copyright law.

>fork be distinguishable and non-confusable

You're mostly talking about trademarks at that point, not copyright.

No, trademarks are irrelevant at this point. The original author of a work retains copyright in that work, regardless of the license under which derivatives are distributed. If they have distributed their work under a lax license and then chose to stop distributing under that license, a pre-existing recipient of that code does not suddenly gain copyright. They can not claim the project as their own or lead users to believe they have copyright in the materials they are modifying and distributing other than as a derived work.

For this to come under trademark legislation, there would have to be demonstrable trade. That's hard to show in the case of free distribution.

I assume that parent meant «shut down the copies of the code under their own control».