SQL Server – Running Out of Disk Space Mid-Restore

What you're trying to do would leave the database in a (transactionally) inconsistent state, hence it isn't possible.

The Partial Database Availability whitepaper is a useful reference guide and includes an example of how to check whether a particular table or file is online. If your data access were through stored procedures, you could relatively easily incorporate that check.

One alternative (but somewhat hacky) approach that might be worth a look in your scenario would be to hide the table and replace it with a view.

-- NB: SQLCMD script
:ON ERROR EXIT
:setvar DatabaseName "TestRename"
:setvar FilePath "D:\MSSQL\I3\Data\"

SET STATISTICS TIME OFF;
SET STATISTICS IO OFF;
SET NOCOUNT ON;
GO

USE master;
GO

IF EXISTS (SELECT name FROM sys.databases WHERE name = N'$(DatabaseName)')
  DROP DATABASE $(DatabaseName)
GO

CREATE DATABASE $(DatabaseName) 
ON PRIMARY 
  (
  NAME = N' $(DatabaseName)'
  , FILENAME = N'$(FilePath)$(DatabaseName).mdf'
  , SIZE = 5MB
  , MAXSIZE = UNLIMITED
  , FILEGROWTH = 1MB
  ) 
, FILEGROUP [FG1] DEFAULT
  ( 
  NAME = N' $(DatabaseName)_FG1_File1'
  , FILENAME = N'$(FilePath)$(DatabaseName)_FG1_File1.ndf'
  , SIZE = 1MB
  , MAXSIZE = UNLIMITED
  , FILEGROWTH = 1MB 
  ) 
, FILEGROUP [FG2] CONTAINS FILESTREAM
  ( 
  NAME = N'$(DatabaseName)_FG2'
  , FILENAME = N'$(FilePath)Filestream'
  )
LOG ON 
  ( 
  NAME = N'$(DatabaseName)_log'
  , FILENAME = N'$(FilePath)$(DatabaseName)_log.ldf'
  , SIZE = 1MB
  , MAXSIZE = UNLIMITED
  , FILEGROWTH = 1MB
  )
GO

USE $(DatabaseName);
GO

CREATE TABLE [dbo].[BinaryContent](
    [BinaryContentID] [int] IDENTITY(1,1) NOT NULL
    , [FileName] [varchar](50) NOT NULL
    , [BinaryContentRowGUID] [uniqueidentifier] ROWGUIDCOL UNIQUE DEFAULT (NEWSEQUENTIALID()) NOT NULL
  , [FileContentBinary] VARBINARY(max) FILESTREAM  NULL
) ON [PRIMARY] FILESTREAM_ON [FG2]
GO 

-- Insert test rows
INSERT
  dbo.BinaryContent
  (
  [FileName]
  , [FileContentBinary]
  )
VALUES
  (
  CAST(NEWID() AS VARCHAR(36))
  , CAST(REPLICATE(NEWID(), 100) AS VARBINARY)
  );
GO 100

USE master;
GO

-- Take FILESTREAM filegroup offline
ALTER DATABASE $(DatabaseName)
MODIFY FILE (NAME = '$(DatabaseName)_FG2', OFFLINE)
GO

USE $(DatabaseName);
GO

-- Rename table to make way for view
EXEC sp_rename 'dbo.BinaryContent', 'BinaryContentTable', 'OBJECT';
GO

-- Create view to return content from table but with NULL FileContentBinary
CREATE VIEW dbo.BinaryContent
AS

SELECT
  [BinaryContentID]
    , [FileName] 
    , [BinaryContentRowGUID]
  , [FileContentBinary] = NULL
FROM
  [dbo].[BinaryContentTable];
GO

-- Check results as expected
SELECT TOP 10
  *
FROM
  dbo.BinaryContent;
GO

Although you had SORT_IN_TEMPDB = OFF, that is not the only thing that uses tempdb. You also had set ONLINE = ON.

Since the job ran 50 minutes before you had trouble, it may be that you had enough activity in that single transaction to fill tempdb with row versioning data. This is described here:

http://technet.microsoft.com/en-us/library/ms179542.aspx

In part it says: "Online index operations use row versioning to isolate the index operation from the effects of modifications made by other transactions. ... Concurrent user update and delete operations during online index operations require space for version records in tempdb."

EDIT: Actually a 200 MB tempdb seems quite small for a database with a 44 GB table.