I don't think he can- at least not as easy as he can sue the deep pocketed Baldwin.
Evidently, the production company was a temporary entity formed by a pool of investors for the sole purpose of funding Rust. Suing individual investors maybe too much of stretch even in the United States.
In the end, that could leave Baldwin as the only deep pockets and the only viable target for the follow on law suits. I wonder......
He likely has enough assets to consider over seas accounts and to hire expert help in setting them up. Evidently, his mega condo / mansion in NYC cannot be sized so long as his wife also lives there. Other assets such as a vacation mansion in Vermont could probably be liquified (Court holds on property sales tied to lawsuits are said to be very rare).
Likewise, my understanding is that Courts are not debt collectors and rarely, if ever, truly compel lawsuit defendants to reveal the extent of their assets. So.... what would happen if AB just walked away from the follow on lawsuits? Could they actually collect anything from him he were to move out of the US- well, in the financial sense?
Or maybe even stay partially in the US? Some states are said to have laws allowing for asset protection trusts that are specifically engineered in the legal sense to be near impossible, or de facto impossible to seize- even with fraudulent transfer considerations