reduced size and added fix for https://stackoverflow.com/questions/1293147/javascript-code-to-parse-csv-data

csvStringToArray.js

const csvStringToArray = strData =>
{
    const objPattern = new RegExp(("(\\,|\\r?\\n|\\r|^)(?:\"([^\"]*(?:\"\"[^\"]*)*)\"|([^\\,\\r\\n]*))"),"gi");
    let arrMatches = null, arrData = [[]];
    while (arrMatches = objPattern.exec(strData)){
        if (arrMatches[1].length && arrMatches[1] !== ",")arrData.push([]);
        arrData[arrData.length - 1].push(arrMatches[2] ? 
            arrMatches[2].replace(new RegExp( "\"\"", "g" ), "\"") :
            arrMatches[3]);
    }
    return arrData;
}

Suggestion to fix the problem with empty cells being parsed as undefined (and some cleanup):

const csvStringToArray = (data) => {
  const re = /(,|\r?\n|\r|^)(?:"([^"]*(?:""[^"]*)*)"|([^,\r\n]*))/gi
  const result = [[]]
  let matches
  while ((matches = re.exec(data))) {
    if (matches[1].length && matches[1] !== ',') result.push([])
    result[result.length - 1].push(
      matches[2] !== undefined ? matches[2].replace(/""/g, '"') : matches[3]
    )
  }
  return result
}

The core fix is in your line 7, though, as arrMatches[2] may be undefined, '', or something truthy. And you want the empty string to also go down the first code path, since in that case arrMatches[3] is undefined.

What exactly is the condition for breaking out of this while statement?

What exactly is the condition for breaking out of this while statement?

When arrMatches value is no longer truthy. aka when RegExp.exec (https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/RegExp/exec) returns null instead of a value.