It is possible to know the line where an application faulted even if it was not running under debugger or memory dump is not available. It won’t probably tell you why it failed, but it will give you at least a point where to start investigating.
After the application failed, look at the Windows Event Logs for an entry like this:
"Faulting application yourapp.exe, version 1.0.0.0, time stamp 0x49e0238, faulting module yourmodule.dll, version 1.1.0.0, time stamp 0x09ec5a57, exception code 0xc0000005, fault offset 0x000000000051000e, process id 0x00, application start time 0x00."