Remove invisible null characters a string's ending
One of the reasons I vastly prefer convert() over cast() is that convert() is much more extensible. For example, you can use a style number to convert a binary value to a string as is. So if 3F00 is always the problematic character:

SELECT CASE 
  WHEN CONVERT(nvarchar(max), @BrokenString, 1) LIKE N'%3F00' 
  THEN 'borked' END;


Result:

borked


So you can find all the offending rows (this will not set any speed records) using:

SELECT ... FROM dbo.table 
WHERE CONVERT(nvarchar(max), column) LIKE N'%3F00';