DECLARE @List NVARCHAR(MAX)

SET @List = '1'

UPDATE MyTable1
SET MyCol = NULL
FROM MyTable(NOLOCK)
LEFT JOIN MyFun(@List) ON a = b
WHERE MyCol IS NOT NULL
	AND a IS NULL

	Executed as user: NT AUTHORITY\SYSTEM. UPDATE failed because the following SET options have incorrect settings: 'QUOTED_IDENTIFIER'. 
	Verify that SET options are correct for use with indexed views and/or indexes on computed columns and/or filtered indexes and/or 
	query notifications and/or XML data type methods and/or spatial index operations. [SQLSTATE 42000] (Error 1934). 
	The step failed.

set quoted_identifier on;

SET ANSI_NULLS OFF
GO

SET QUOTED_IDENTIFIER OFF
GO

CREATE PROCEDURE ...
AS
EXTERNAL NAME ...

Процедуру CLR я изменить не могу.

ALTER FUNCTION MyFunction(@str [nvarchar](max))
RETURNS  TABLE (
	[IntValue] [int] NULL
) WITH EXECUTE AS CALLER
AS 
EXTERNAL NAME [UserDefinedFunctions].[StringSplitFunctions].[SplitIntList]

Column name             Data type      Description   
uses_quoted_identifier  bit            Module was created with SET QUOTED_IDENTIFIER ON.