What is the small round metal "ball" mounted to the front of the sub-assembly cross member?

I'm not sure. But after a Google Image search for the part number of the cross member, I found these pictures (2008 Toyota Prius Sub Frame - 51201-47030 - Used - A Grade.)
It looks like a absorber for a special frequency. So for a proper function the correct mass and the right stiffness of the rubber is needed. Normally the rubber is vulcanised directly to the metal. Maybe a good adhesive will do, but I doubt that it will last forever.
The cube in the near seems to be an absorber, too, but of course for another frequency.
I think these absorbers are only for a better comfort and not for a longer lifetime of the cross member and the nuts and bolts (fatigue stress).
If there appears a NVH problem in the late development process, an absorber or damper is often the right solution to reduce a "boom"/"eak"/rattle occurring in special situations.
For lifetime issues such an absorber for a fix frequency is too risky. At the one hand often you can't reduce the problem of fatigue to one frequency, because the parts are stressed with different frequencies from ignitions and tooth wheels and so on, and reducing only one of them won't help a part living much longer (except it's the eigenfrequency, but this can be changed easy) and on the other hand Temperature and ageing changes the frequency of the absorber and reduces it's function. And a lost absorber can't work, too.
Only my personally theory! So I, personally, would try some powerful adhesive and if it's getting lost, ¯\_(ツ)_/¯


SM-G900F ?

 

That seems to me it came out from a failed engine mount.
We of those have some stuff like grease embedded in them. If that stuff isn't in the engine mount you removed it again, replace the mount. You'd probably start hearing clunky noises now.

Dxta

 

Maybe it was hit with jack when lifting the car at some point. Or maybe it was hit with somethong on the road. If this was my car I would probably just leave it out. It’s there to reduce some vibration but probably you won’t feel any difference. And it’s very unlikely that the vibration would be strong enough to brake anything.

No it’s not. See the link that MickyMatter posted it’s a mass damper.

 

I was mostly thinking that if somebody didn’t know or accidentally jacked from wrong place. But I didn’t really look into it so maybe it’s actually not possible.

But that won’t change my opinion about the part. If actual engine mount is ok I would just leave that part out.