I have a console-mode Windows application (ported from Unix) that was originally designed to do a clean exit when it received ^C (Unix SIGINT). A clean
This could be due to the infamous mintty "Input/Output interaction with alien programs" problem (aka mintty issue #56). In this case it is manifesting as Ctrl-C abruptly killing the program rather than being passed down to the program as a signal to be caught and handled. Evidence for this theory is based on zwol's extensive explanation: "console-mode Windows application", "[application is] designed to do a clean exit when it received ^C", "[application] works correctly when the program is run under CMD.EXE" but "[when using the terminal] that comes with MSYS [...] program is forcibly terminated" (at the time of writing (2018) MSYS defaults to using mintty as its terminal).
Unfortunately mintty isn't a full Windows console replacement and various behaviours expected by "native" Windows programs are not implemented. However, you might have some joy wrapping such native programs in winpty when running them within mintty...
Other questions also describe this behaviour: see https://superuser.com/questions/606201/how-to-politely-kill-windows-process-from-cygwin and https://superuser.com/questions/1039098/how-to-make-mintty-close-gracefully-on-ctrl-c .