I guess some signals will be sent to the process. Some or one? If more than one in which order do they occure?
And what happens if the Terminate button is pressed and if the process has forked? And what happens if the process has started other processes by system(...)?
I can't be sure without checking, but I would be surprised if the signal sent was anything other than SIGTERM (or possibly SIGKILL, but that would be a bit unfriendly of CDT).
As for sub-processes, depends what they are actually doing. If they are communicating with their parent processes over a pipe (in any way whatsoever, including reading their stdout), they'll likely find that those file descriptors close or enter the exception state; if they try to use the fds anyway they'll be sent a SIGPIPE. There may also be a SIGHUP in there.
If a sub-process was really completely disjoint (close all open FDs, no SIGTERM handler in the parent which might tell it to exit) then it could theoretically keep running. This is how daemon processes are spawned.