### Please describe the problem.
I found one of my repos damaged after letting the webapp sync with it for a while.  The filesystem inodes were exhausted and all the refs pointed to objects that do not exist.

### What steps will reproduce the problem?
I expect this issue to be reproduced by syncing to a filesystem without enough free inodes to hold the incoming files.

### What version of git-annex are you using? On what operating system?
This repo is using git-annex 6.20160229-g37a89cc

### Please provide any additional information below.

[[!format sh """
# If you can, paste a complete transcript of the problem occurring here.
# If the problem is with the git-annex assistant, paste in .git/annex/daemon.log

$ git status
fatal: bad object HEAD
$ git pull
error: refs/heads/master does not point to a valid object!
error: refs/heads/synced/git-annex does not point to a valid object!
error: refs/heads/synced/master does not point to a valid object!
error: refs/heads/master does not point to a valid object!
error: refs/heads/synced/git-annex does not point to a valid object!
error: refs/heads/synced/master does not point to a valid object!
error: refs/heads/master does not point to a valid object!
error: refs/heads/synced/git-annex does not point to a valid object!
error: refs/heads/synced/master does not point to a valid object!
error: refs/heads/master does not point to a valid object!
error: refs/heads/synced/git-annex does not point to a valid object!
error: refs/heads/synced/master does not point to a valid object!
remote: Counting objects: 3, done.
remote: Compressing objects: 100% (3/3), done.
remote: Total 3 (delta 0), reused 0 (delta 0)
Unpacking objects: 100% (3/3), done.
error: refs/heads/master does not point to a valid object!
error: refs/heads/synced/git-annex does not point to a valid object!
error: refs/heads/synced/master does not point to a valid object!
fatal: bad object HEAD
error: /home/olpc/annex-ext4 did not send all necessary objects

Auto packing the repository in background for optimum performance.
See "git help gc" for manual housekeeping.
error: The last gc run reported the following. Please correct the root cause
and remove .git/gc.log.
Automatic cleanup will not be performed until the file is removed.

error: refs/heads/master does not point to a valid object!
error: refs/heads/synced/git-annex does not point to a valid object!
error: refs/heads/synced/master does not point to a valid object!
error: refs/remotes/beta/master does not point to a valid object!
error: refs/remotes/beta/synced/master does not point to a valid object!
error: refs/remotes/halloween/master does not point to a valid object!
error: refs/remotes/halloween/synced/master does not point to a valid object!
fatal: bad object HEAD
error: failed to run repack

# End of transcript or log.
"""]]

### Have you had any luck using git-annex before? (Sometimes we get tired of reading bug reports all day and a lil' positive end note does wonders)

I'm running into a few issues but I intend to work through them.