If sqlserver process is killed while running some heavy operations, the database usually goes InRecovery mode. The is an auto recovery process. The database gets in normal mode after a while. However, you can see progress of the auto recovery proces by running the following statements.
SELECT sqltext.TEXT,
req.session_id,
req.status,
req.command,
req.cpu_time,
req.total_elapsed_time,
req.percent_complete
FROM sys.dm_exec_requests req
CROSS APPLY sys.dm_exec_sql_text(sql_handle) AS sqltext