There is no need to resort to looping for this. You can instead use STUFF.

Thanks Mark for the ddl and sample data.

declare @a table (Linenumber int, ErrorText varchar(30),FileID int)

insert into @a values

(1, 'a', 10),

(1, 'b', 10),

(2, 'a', 11),

(2, 'b', 11),

(2, 'c', 11),

(3, 'c', 12),

(3, 'd', 12)

select Linenumber,

STUFF((select ',' + ErrorText

from @a a2

where a1.Linenumber = a2.Linenumber

order by a2.ErrorText

for xml path('')), 1, 1, '') as ErrorTexts

, FileID

from @a a1

group by Linenumber, FileID