Technically speaking, the bearing sits in that housing. The axel goes through the inner race of the bearing. The bearing housing that actually captures the outter race of the bearing seems to be ok. I am doubtful, the way it looks, that you would get much movement out of the bearing, thereby the axel as long as the bearing "seats" inside the housing correctly. BUT, I would be nervous AF any time I hopped on that bike. You probably would never have an issue as long as whoever put the tires on always made sure it was balanced to compensate.
I've seen this done more than once from someone trying to "knock" a bearing out of a wheel. Shit happens.
That being said...What year is the bike? Where are you? I have a set of wheels I pulled of my 12 Ultra that have been sitting in my basement for MANY MOONS.