SQL shouldn't shut down due to lack of space, unless something bad went wrong in the system DBs. It would normally just roll back the offending transactions, at most make the databases read only if the logs are full.
Can you check the SQL error log, look for messages relating to the shutdown?
Gail Shaw
Microsoft Certified Master: SQL Server, MVP, M.Sc (Comp Sci)
SQL In The Wild: Discussions on DB performance with occasional diversions into recoverability