This was asked back on Slashdot 14 years ago in 2000. As you can see, most of the websites mentioned that archived "ummaintained" software have since evaporated and are unmaintained themselves!
Then it was talked about briefly on stackoverflow in 2009.
Submitter, what I suggest you do is include a text file that describes the history of the project (If it was me - I think it would be nice to thank those by name who made significant contributions), known issues, ideas for direction of the project (if any), and then post it to Github and Sourceforge as an 'ummaintained' software. With as permissive as a license as you can give it, which will encourage it's use down the road. Also, I would post links, notices, and intentions to any associated forums. And give the community as much time to as possible before closing the website down. Maybe someone or some company will have the where with all to continue the project. If it is reasonable to do so and they seem to be reputable and serious, you might let them. Otherwise, when finished, make sure that archive.org has browsed the website for their archives. Also, post a copy the final software there. If it has a domain name, if you can, I'd give it a ten year renewal date and give it a notice of closure and a link to the project on Github.
But the larger issue for me, is that you, your colleagues, and friends spent time and effort on this project. That should be recognized. At least by acknowledging that support is ceasing for this project, it can hopefully move on to other hands in the future. It does happen.
I wish more more programmers were as thoughtful as you. And I wish there were better ways (i.e. more permanent and standardized) of dealing with orphanware.