track down which application / procedure / function modified the value of a column in a specific table
This might get you going along the right track. You pass the sql_handle of the existing connection to the table valued function sys.dm_exec_sql_text, and it returns the SQL text being executed.  If you run this example you will see your own code, as @@SPID is your own process ID.

Source Article

SELECT t.text
FROM sys.dm_exec_requests AS r
CROSS APPLY sys.dm_exec_sql_text(r.sql_handle) AS t
WHERE session_id = @@spid


Other system resources that may help you on your quest:

select * from sys.dm_exec_connections where session_id = @@spid
select * from sys.dm_exec_sessions where session_id = @@spid
select * from sys.dm_exec_requests where session_id = @@spid