In Alberta, livestock is still considered to be owned by the original owner, even if it has gotten out of a compound or field, and considered their property.
Might be different in other provinces....
Cat
And the owner of at large livestock is responsible for any damages done by the livestock.
These animals are exotic wildlife. They may interbreed with the local deer and introduce genes, parasites, and disease that could decimate the local deer herd. Even by eating and leaving scat piles, or if one gets killed and eaten by predators any exotic parasites may get into population.
We have Chronic Wasting Disease in Alberta. There are strong indications that this disease was brought in by game farmers importing infected animals from Colorado then spread to the wildlife. But like BSE know one knows the transmission vector yet, or whether it is endemic in the population and brought out by an environmental factor, or whether diseases like this happen from a spontanious mutation in the virus or prion world of almost alive long chain molecules.