Let's say a company issues an interim earnings report and FactSet simply ignores it. In that case, there's no way for Portfolio123 to know about it, and no way for the report to be mentioned anywhere in the system.
On the other hand, let's say a company issues an interim earnings report and FactSet takes four weeks to process it. As soon as the report is issued and FactSet records that fact in its database (which is usually very quickly), Portfolio123 gives the stock a StaleStmt = 1 until the report is processed.
DaysLate is quite different. This is populated when it has been a certain number of days since the latest (FactSet-acknowledged) earnings report. So you will see some companies who have issued reports but whose reports have been ignored by FactSet with DaysLate > 0. However, DaysLate was designed for US stocks and really shouldn't be used for European stocks.
If you want to avoid stocks whose data FactSet has not yet processed, use StaleStmt = 0 in your buy rules or universe rules. But there's no way to automatically avoid stocks whose earnings releases FactSet missed altogether.