The maintainer will fork the project under a new name, and continue to work for it. GNU will be left with a piece of software that slowly bitrots and becomes outdated, unless it can attract someone else to take it over.
And the cost of obsolete code is not a bit of web storage; it reflects on the project as a whole. The GNU userland tools have been important for Linux. But what happens if people move to different user land tools?
It's not super important, but it is a shame that people leave projects.
Perhaps if free software and open source software had invested in a bunch of diplomats to translate the flames between De Raadt, Torvalds, Stallman, etc things would look very different today.
There are other options than the two you've outlined. What if they find someone to maintain it, who isn't that good? How come the GNU Hurd hasn't yet been disposed of?