Do you mean that you get the “Cubase is unstable after crashing bla bla please save your project and restart Cubase”, then you save and get the message “The file has been renamed projectXYZ-01.cpr…” or something close to that?
I have never had any trouble opening these files.
It indicates that there’s some particular thing in your system that always causes a crash and that this something sticks when you then save, causing the invalid file.
The only time I can remember that I got the “invalid project”-message, I think I just tried to reopen it one or a few times and it would eventually open. It was caused by me accidentally pasting automation data onto a marker track I think.
Please provide some details about your system (put it in your signature) and give us some examples of how your projects are set up, plug-ins used, workflow that seems to trigger the crash and similar useful stuff. It makes it easier to help.