Hello Howard,
thanks a lot for your help!
I tried before the following code; and now it works fine. I have no clue what the problem was, because the only thing I did was to delete the first read of the file and the first put to the array in the loop; and therefore a change in the loop conditions from a check of an empty input string and the error to only the error check.

Code:

Dim $F01Handle
Dim $F01RC
Dim $F01Line
Dim $F01Index
Global $KatArray[100]

$F01Handle = FreeFileHandle ()
 
$F01RC = Open($F01Handle, "BLOCKED-KATEGORIEN.TXT",2)

$F01Index = 0

While @ERROR = 0

		$F01Line = ReadLine($F01Handle)
		$KatArray[$F01Index] = $F01Line
		$F01Index = $F01Index + 1
	
Loop

ReDim Preserve $KatArray[$F01Index]

$F01RC = Close($F01Handle)

EndFunction