In the sacred texts of the Hebrews and Christians there is a story about the times when everybody spoke the same language. The engineers were having a grand time, making buildings and cities and generally improving life for everybody. Then the managers showed up and determined that everybody should be working to show that they were almost as good as God Himself. God didn't take kindly to that corporate goal, so He made people start to speak different languages. Engineering communication has been difficult ever since.
Regardless of place of origin, the consensus is that Data Sheets should include a section about "Absolute Maximum Ratings" - the conditions that are likely to cause permanent damage to the component. Data Sheets will also show "Performance Characteristics" - the behavior you should expect from a device, under some closely specified conditions.
Sometimes it is difficult to separate the measured performance values, from the conditions under which the measurements were made . . . .and I think the BL8555 Data Sheet is a prime example of that problem. The word "arbitrary" appears on pg 4 with a reference to "output voltage". This seems to say that the behavior described in the following table applies equally to all of the output voltage variants of the BL8555.
I believe the first line of the table doesn't belong in the table. Taken literally, it implies that the BL8555 can make its input voltage range between 1.8V and 8V. Rather, it should be made clear that all subsequent lines of the table describe behavior when the input voltage is between 1.8V and 8V.
(And the "1.8V" value doesn't make sense. Obviously, if you have the version of the BL8555 that regulates to 5.0V, then most of the entries in the table have no meaning if the input voltage is only 1.8V. Instead of 1.8V, the entry for minimum input voltage should be something like "Vreg + Vdropout".)
I'll stick to my earlier statement that this device was intended to operate only up to an input voltage of 8V. With higher input voltages, all bets are off. I can hope that the device doesn't misbehave as severely as some of the examples I previously listed, but I've done enough circuit design to know that each of those examples is a possibility.