Not that low a speed. Let’s say the generational ship was moving 0.01c, at the low end of what’s believable (500-1000 years to a nearby star). That means the ship was decelerated 99.999% of the way from cruise speed before jettisoned. In terms of energy, that’s 99.99999999% of the stopping thrust already expended. That’s without even getting into the rocket equation which makes it even worse.

At that point why not carry it into the system with you? The mass would be negligible given the energy budget. Ejecting it seems to serve no purpose but wasting several cubic kilometers of presumably processed material. Why do that?

Now maybe it was a probe ejected from a ship at distance, but then why is it tumbling end over end?