I'm not sure what you're asking, possibly because you might be using incorrect terminology.
Project = individual entities with a stated goal for the science they are researching. For exmaple, SETI@home, Einstein@home, ClimatePrediction.net are all exmaples of projects.
workunits / tasks = the individual files sent to your computer to be processed, with results uploaded back to the project's servers.
So, reading your question with the first meaning, you can find what a project has concluded once the research has been completed. This may be different for different projects. For example, SETI@home only has one stated long-term goal: to find an intelligent signal from an extra-terrestrial source. The project can only give an update once the signal has been found and confirmed. Einstein, on the other hand, is constantly finding new pulsars and quasars, and can make announcements accordingly.
But if by project you mean workunit or tasks, how can you find what has been concluded in the SETI@home work you upload, that is what the Near-Time Persistency ChecKeR (NTPCKR, or "nit-picker") is for. The NTPCKR is an automated process that scans the Master Science Database for all returned results to find the most interesting signals that can possibly be re-observed for confirmation.
The problem is the lack of funds to employ programmers to keep the NTPCKR running constantly, so it isn't always running as well as it should. You can find the results of NTPCKR here.
Do either of those explanations answer your question?