As others have said (and will say), no, if the program does not inherently support picking up where it left off, then there is no practical (possible?) way to continue either the program from where it ended or converting a video in the middle.
One less practical, but not too horrendous method that may work for you is to use a virtual machine.
If the program does not inherently support resuming from where it left off, then one way to fake it is to restore the state of the program to that of where it was when it was exited. Normally, there is no practical way to do that with a program in Windows (even resuming from hibernation does not technically put everything back exactly the way it was when it went to sleep). However, a virtual machine can save its state and resume where it left off.
- Install a copy of a virtual machine program like VMWare Player, Virtual PC, or VirtualBox (XPMode comes with Windows 7 Ultimate)
- Install a copy of Windows in there
- Install Handbrake in the guest OS (the Windows in the VM)
- Set up a shared or networked folder so that the guest OS has access to the video file on the host (that way you don’t have to bother copying it to the guest)
- Finally, configure the VM so that when it is closed, it is put to sleep and the state is saved
Now, whenever you leave the computer unattended and others close it, they are not actually closing the program, they are closing the whole guest OS, but when you come back to the computer, you can simply run the VM software and load the guest OS and find that the video-conversion program is exactly where it left off, and so long as the source video is still there, it should happily chug along without issue (though you could even avoid that problem by copying the source video to the guest OS).
I got this idea because of game emulators. Years ago, I found level five of the original Castlevania game to be frustratingly difficult, so I gave up trying to play it in my NES and played it in an emulator instead. That way, I could save and restore the state, which made it much easier since I did not have to keep starting the whole level over. Since then, I have been frustrated by scenarios such as yours on numerous occasions and have thoughts of ways to overcome it through the use of emulators and virtual machines.
As a side note, here are a few alternate solutions to your specific problem, the practicality of which depend on your specific situation:
- Lock the system with a screensaver/login password when you leave
- Create another account for others to use and switch to that account when you leave
- Set permissions to prevent the ability to close the program
- Use a window-manipulation tool to remove/disable various aspects of Handbrake like its taskbar button, its close button (
☒) or even the whole window
- Minimize the program to the notification area/hide the program completely
- Place a post-it note on the monitor
- Just tell/ask/beg the others to knock it off