If there are two existing species reproducing separately, you will not find a parent in one group producing offspring that belong to the other group. Never. The best you could get is a hybrid of the two. And there are documented cases in which such a hybrid has proved fertile and become established as a third species which does not interbreed with either of its parent species.
Such hybridization is one way to get a new species, but I would call that crossing from one species to another.
The other way to get a new species that we have discussed is through population isolation. A single species is split into two species. This has also been documented both by experiment and in nature. And I don't think that can be called crossing the boundary either. It is more in the nature of erecting a boundary where there was none before.
The other way for a species to change is by phyletic gradualism. This is a gradual accumulation of changes in one species such that the species at the end of the transformative process is different from the initial stock. When phyletic gradualism occurs over time, it has to be inferred from the morphology of fossil sequences as one cannot directly test whether the newer species could or could not interbreed with the ancestral species. But we also see examples of phyletic gradualism in which all the gradations from one species to another are contemporaneous. Such sequences are called "ring species".
"The Arctic Ocean polar ice cap limits the species range of Sea Gulls to its periphery. Races from Siberia freely interbreed with races from America. Races from America freely interbreed with races from Europe. Going the other way, Races from Siberia freely interbreed with races from the Caucauses. However, Western European herring gull (
Larus argentatus) do not interbreed with the lesser black-backed gull (
Larus fuscus) from Centrial Europe where these races of Sea Gulls occur together in northern Europe. So, all along the ring that circumnavigates the globe about the Arctic there is gene flow but where the two ends of the ring meet in Europe there is no gene flow."
f26 Phyletic gradualism
This is the closest example I can find of "crossing the boundary from one species to another" yet that description doesn't really seem to fit here either.
I don't know of any other way that new species evolve, so perhaps you are barking at a bogeyman that doesn't really exist in nature.