Control which process gets cancelled by Ctrl+C

I have a live CD that boots into Linux and runs a small Bash script. The script searches for and runs a second program (which is usually a compiled C++ binary). You're supposed to be able to abort the second program by pressing Ctrl+C. What should happen is that the second program halts, and the Bash script continues running cleanup. What actually happens is that both the main application and the

[uraxurax]

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[riywo]

長年の謎が解けた。。。