Externality is a real concept and so are subsidies, but "failure to take action against some party imposing costs on others" doesn't amount to a subsidy of that activity
Like, if the government fails to crack down on illegal drug distribution and all its associated externalities, is that a subsidy? Where does it end? It's nonsense.
I don't think it makes sense to slice up society into tiny divisions and categorize each one like that. For example the government takes affirmative action to create the concept of land ownership and corporations. Those legal fictions then assist for example this polluter.
I concur in principle in consistent word usage, but I'm not aware of one other than externalities for this issue, and that is too vague to convey the fact that public money is spent in support of their profit.
The War on Drugs helps subsidize the cartels and drug dealers by creating a market that only they can fulfill. We pay an obscene amount of money for sustaining that market.
It's semantics: instead of giving money directly to the organization, let them make money and have the public money be spent to clean up the mess they made. Same difference: private profit and public expenditure for it.