First of all, please don't use a shell script for this sort of task, it is slow and error prone. In any case, grep can do what you want already:
grep -f BlockspamCLIs.txt *_All_events.csv >> output6.txt
From man grep:
-f FILE, --file=FILE
Obtain patterns from FILE, one per line. If this option is
used multiple times or is combined with the -e (--regexp)
option, search for all patterns given. The empty file contains
zero patterns, and therefore matches nothing.
-f FILE, --file=FILE
Obtain patterns from FILE, one per line. If this option is used multiple times or is combined with the -e (--regexp) option, search for all patterns given. The empty file contains zero patterns, and therefore matches nothing.
Next, if you do use a shell loop to iterate over the contents of a file, never do it with for i in $(cat file). And, you must always quote your variables to avoid various problems. For example, your command won't work if any of the lines in BlockspamCLIs.txt contain whitespace.
That said, if your lines don't have spaces or shell globbing characters, the command you show would work. It would be better written like this:
while IFS= read -r i; do
grep -e "$i" -- *_All_events.csv >> output6.txt
printf '%s\n' "$i"
done < BlockspamCLIs.txt