That gets tricky.
Let's use the Snow Ravens as our example, for no better reason than I've been painting a Zeta Galaxy Kit Fox E. The Ravens jump in and help the Jaguars. They succeed, but the Jags are shown to be weak and to be absorbed. Here's where it gets messy. The Ravens might claim it, but they jumped in- didn't they commit a dezgra act by interfering in a Trial which they had no involvement in? This kind of stuff lead to the Reaving a decade later, after all.
But, for sake of argument, sure, the Ravens do it. They absorb the Jags. If that's the case, yes, they gain all Jaguar personnel, assets, and posessions- which, yes, would include the invasion corridor... assuming Bulldog ALSO failed, and the invasion corridor still exists, of course. In that case, the Jaguar OZ becomes the Raven OZ (and likely immediately be subject to Trials of Grievance and such, because have you ever met the Clans before?)