SQL Server 2017

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create table #tmp 
(
  id    int identity(1,1) not null,
  plist varchar(max) null
);

create table #tmpprod 
(
  oldid int null,
  newid int null
);

insert into #tmp(plist) values
('10,11,15,17,19'),
('22,34,44,25'),
('5,6,8,9');

insert into #tmpprod(oldid, newid) values
(5,  109),
(9,  110),
(10, 111),
(15, 112),
(19, 113),
(30, 114),
(34, 222),
(44, 333);
11 rows affected

CREATE FUNCTION [dbo].[SplitInts]
(
   @List       VARCHAR(MAX),
   @Delimiter  CHAR(1)
)
RETURNS TABLE
AS
   RETURN ( SELECT Item FROM ( SELECT Item = x.i.value('(./text())[1]', 'int') FROM 
            ( SELECT [XML] = CONVERT(XML, '<i>' + REPLACE(@List, @Delimiter, '</i><i>') 
              + '</i>').query('.') ) AS a CROSS APPLY [XML].nodes('i') AS x(i)
          ) AS y WHERE Item IS NOT NULL
   );
/* <= SQL Server 2016 */

;WITH x AS
(
    SELECT id, item, oldid, [newid], rn = ROW_NUMBER() OVER
    (PARTITION BY id ORDER BY PATINDEX('%,' + RTRIM(s.Item) + ',%', ',' + t.plist + ','))
    FROM #tmp AS t CROSS APPLY dbo.SplitInts(t.plist, ',') AS s
    LEFT OUTER JOIN #tmpprod AS p ON p.oldid = s.Item
)
SELECT id, newlist = STUFF((SELECT ',' + RTRIM(COALESCE([newid], Item)) 
    FROM x AS x2 WHERE x2.id = x.id
    FOR XML PATH(''), 
    TYPE).value(N'./text()[1]', N'varchar(max)'), 1, 1, '') 
FROM x GROUP BY id;


id
newlist


1
111,11,112,17,113

2
22,222,333,25

3
109,6,8,110


/* >= SQL server 2017 */

;WITH x AS 
(
  SELECT o.id, val = COALESCE(n.newid, p.value), p.[key] 
  FROM #tmp AS o
  CROSS APPLY OPENJSON('["' + REPLACE(o.pList, ',', '","') + '"]') AS p
  LEFT OUTER JOIN #tmpprod AS n 
  ON p.value = n.oldid
)
SELECT id, newlist = STRING_AGG(val, ',')
  WITHIN GROUP (ORDER BY [key])
  FROM x GROUP BY id;


id
newlist


1
111,11,112,17,113

2
22,222,333,25

3
109,6,8,110