I noticed that FabCam crashes when try to access to the webcam in Google Chrome on Windows 7 64bit. This doesn't depend from FabCam, but depends from flash player settings.
To solve the issue you have to go to chrome://plugins/ in flash section, you need to disable the other plugins and keep enabled C:\Windows\SysWOW64\Macromed\Flash\NPSWF32....dll
You can see this video that i found on youtube to clarify the process: How To Fix Flash Crashes in Google Chrome
Let me know if you still have problem and/or if you can't solve with this solution.