Filegroup preventing log file from backup

We have a intimidating problem with a production database.
The database have db file situated on primary drive and log file on a secondary one.
The primary drive contains two file group - one for primary DB file and one small FILESTREAM typed group for memory based objects.
The secondary drive contains db log file.
Since some moment the first drive run out of physical space as a result of autogrowth process. The issue is log backup also stopped working at the moment because of the error:

The operating system returned the error '112 (There is not enough space on the disk.)' while attempting 'FsLogMgr::LogInternal:CreateFile'...
At this point transaction log backup is cancelled due to the error. The file group causing the error is the small and currently unused filestream group. It could be dropped easily, but when attempting to remove the filegroup I have different error:

Drop failed for FileGroup [...]
The container can not be dropped because changes exist that require a log backup.  Take a log backup and then retry the ALTER DATABASE operation. (.Net SqlClient Data Provider)

So the issue has circular nature. I cannot do log backup without dropping the filegroup. But I also cannot drop / take offline the filegroup because the operation requires log backup. So the log is growing uncontrollably and the system is heading towards complete failure.

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Scott PletcherSenior DBACommented:
For now, I'd add another file to the data filegroup to give it sufficient space to begin working again.  Naturally the new space can, and will be, on a different drive.

If you want to, later you can remove the extra file from the data filegroup.

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Microsoft SQL Server 2008

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