I ran into this issue today, and have yet to find any way to catch this exception. Highly disappointed by this.

Although this reply comes two years after the fact, this thread is still relevant, so here's my solution for dealing with arbitrarily large input files. This only applies specifically to splitting lines by \n or \r. More complex regex patterns will need some tweaking.

Below, allLines will become the final List containing all lines (go figure). divideString is a recursive method for breaking the input file into managable chunks, splitting them and appending to a global list. I think this will retain the original line order, but haven't checked yet so beware.

    public List<String> allLines {get; set;}
    private Integer inputCharacterMax { get { return 100000; } set; } // this is a somewhat arbitrary character limit

    public void divideString(String input) {
    	
    	Integer pivot = input.indexOf( '\r', Integer.valueOf(Math.floor(input.length() / 2)) );
    	
    	String left = input.substring(0,pivot);
    	String right = input.substring(pivot);
    	
    	if ( pivot < inputCharacterMax ) {
   	   	// split left and right chunks, add to allLines
    		List<String> leftLines = left.split('\r');
    		List<String> rightLines = right.split('\r');
    		allLines.addAll(leftLines);
    		allLines.addAll(rightLines);
    	}
    	else {
   	   	// divide and conquer!
    		divideString(left);
    		divideString(right);
    	}
    }

 To initiate the process:

Integer pivot = fileContents.indexOf( '\r', Integer.valueOf(Math.floor(fileContents.length() / 2)) );
if ( pivot > inputCharacterMax ) {
	divideString(contents);
}
else {
	allLines = contents.split('\r');
}

 Just managed to process a CSV with over 21,000 rows, and governor/script limits stayed within reasonable values!

If only this exception were catchable, this code would be simplified to begin recursion in a catch, rather than relying on an arbitrary character limit conditional.

Hope this helps someone out there!