tsql to know when a database was last shrunk
Because for shrinking of database one uses DBCC SHRINKDATABASE or DBCC SHRINKFILE, you can try to solve your problem with server audits from the group DBCC_GROUP (see http://technet.microsoft.com/en-us/library/cc280663.aspx and http://msdn.microsoft.com/en-us/library/cc280386.aspx)