Sure, the developer can decide to release the code as open source. That's fine. But to make an open source project requires a lot more commitment than that[1].
An open source project is kinda like a startup. You need your product (the code) you need your marketing (letting people know the code exists) you need your customer development (is the code useful for a lot of developers?) you need sales (dude, you really want to help with this code!) you need passionate early adopters (dude! you actually wrote unit tests for us? Tubular!) etc.
Compared to all that, putting the code up on github is the easiest part.
Really, starting an open source project is about building a community of people. Not people who use the code, but people who care enough about the code to maintain it and contribute to it.
If you don't do that, you've still got abandonware, its just that the code was open sourced before disappearing, never to be seen again.
Spending this effort to build a community may not be viable for projects being shut down- especially if they are failures. The people behind them may be burned out or soon to be unemployed or soon to be handcuffed by NDAs.
Maybe the open source community could use its own equivalent of the ASPCA-- the American Society for the Prevention of Cruelty to Abandoned Projects.
They could take them in, like pets, give them a home for a few months or maybe a year. IF the original developers are willing they can provide as much or as little support as they are emotionally or physically capable of. After a year, if the project has attracted enough interest it is spun out as its own open source project, and if not, it is "euthanized" by being marked as shut down and put in cold storage.
This, at the very least, would serve to bring light to these projects that could use some love. And since the organization would only handle a limited number of projects at a time, they could provide life support during that transitionary year, without burning themselves out trying to save every abandoned project, lost and starving on the side of the road.
[1] I speak theoretically, I'm in the process of making my first open source project and have been thinking about this a lot lately. My previous open source experience has been as a contributor.
Edit to add: this isn't meant as a commentary on Copycopter, just general thoughts on the topic of "don't shut it down, open source it."