Disk became full, had to force shutdown, now it doesn't boot Don't know why I didn't get a warning about disk being almost full... It came down to zero free space and I couldn't do anything except force-shutdown it. I booted into Windows, deleted some files from OSX drive, but now on boot there is a progress bar every time and when it reaches the end (in 15 min), the computer shuts down.

I went into the recovery mode and tried to repair the disk, but it says "The Disk Utility cannot repair the drive... backup files and reinstall the OS" -- something like that.

I have a time machine backup but I'm currently not at home - going home in 3 weeks.

Is it "normal" that system gets borked like this because of full disk + force shutdown? Seems too fragile to me. I have Mavericks 10.9.4 on this system.

Is there anything I can do?
The problem is that the system goes into a fail-safe mode when the directory structure cannot be presumed to be safe for a new write.

You did the correct triage step by booting into recovery mode and attempting to repair the volume with Disk Utility.

At this point, you should back up any files you need. Test that your backup is complete and run Disk Utility against it to make sure it's in a good state.

Then you can boot to recovery and erase the volume or perhaps use another tool to repair the volume. If the drive erases and takes a format - the problem was a directory (data) corruption and not a hardware issue. If the disk can't be erased, then you need to repair the machine before restoring your backup onto a clean install of the OS.

In your case, you could possibly back up the changed files since 3 weeks or just get a new external drive and use Disk Utility to clone the volume or terminal to copy what you can using rsync or another tool.