They tend to rot on my system. The problem is that no-one really wants to pick up someone else's half-finished work unless they know the person really well and believe in the project, which is unlikely since they'd already be working on it and it wouldn't be dead if that were the case.
I keep them. Some of them I revive a few years later (possibly on a different OS). Some others that don't get revived may still have useful pieces of sample code.
If I can't properly develop and support them, they go to that big hard drive in the sky. I take the approach of failing as fast as possible. If code is in this state, it is now failing. It's time to move on to bigger and better things and not waste mental cycles (even minimal) or resources maintaining.
They go on my GitHub. Most as public, some as private. The only ones that stay private are the ones that have some code I worked on for weeks solving a very specific problem that I may use at some point in the future for a business.