I've ruined a rear differential drain plug like this before. This happens especially if you don't have the allen all the way in there (if for example there's rust or scale build up in the bore of the hex), then you're very quickly on the route to stripping it like this. It then no longer "bites" and just turns in place. In my case I used a 25 inch breaker bar and an 18 inch ratchet and it still wouldn't budge. I would put a huge amount of pressure on the bar and it would just flex, it eventually stripped. So now I had both the fill and drain stuck but the drain was stripped.
Want to know how I got it out after I stripped it like your picture shows?
I got an allen socket of a slightly smaller size (for example in SAE when the original size was metric). That let me get a little deeper in to get some more grip on the faces of the hex I hadn't ruined, this was just so that it would be less likely to "turn" itself out. Then the most important part was I hit the drain plug with my MAPP torch (yes that cheap 65.00 one from Home Depot).
After hitting it with a MAPP torch I was able to unscrew it with a regular 9 inch ratchet without having to push on it even a fraction of how much pressure I put on the breaker bar that made the breaker bar flex. That's how much of a difference that torch made. I find that in almost every case I need heat, the MAPP works just fine. Then I torched the fill plug that wouldn't come off before, guess what? Same result, came right off.
For the front differential I learned my lesson on the rear, tried a little bit of pressure, no give, stopped right there and hit both the fill and drain plugs with the MAPP torch, out they came without stripping anything that time at all.
So I don't even bother without the torch on those things any more, it's a waste of my time. The other advantage of the MAPP torch is it heats the drain plug enough to break whatever corrosion is holding it in place but not hot enough to destroy the magnet, since intense heat affects magneticity or even causes certain magnets (like the dark gray ones they usually use on OEM drain plugs and pans) to shatter.