Yes: new management can't un-open-source something. If it's out there, it's out there. They could close future work, but not existing work.

If they employ the core team, and own the immaterial rigths, they could

1. Make next version propietary, or particially propietary

2. Keep updating the closed version, no more core team for open version

3. After some time the open version is too oudated, too far behind the propietary version

4. Ambiquity on lisencing also deteriorates intrest

For examples see, Qt, MySql, Java

It's true that the health of an open source fork isn't guaranteed when there's a split, but OpenJDK looks healthy? I haven't been following Java much.

Yes, and could damage the product/brand in the process. mysql, openoffice, and oracle come to mind. It is survivable but often not a win in the long term for the original author. Seems like a personal decision however.