The first clause of the sentence is not grammatically correct. It doesn't have a verb. It should say: Korean government care packageS ARE BEING GIVEN to people who are in quarantine due to exposure, OR Korean government care packageS HAVE BEEN GIVEN to people who are in quarantine due to exposure, "Ensuring" or "ensuring that" is a conjunction that is connecting the two independent clauses

Nhi: That’s not a sentence, so it’s impossible to say exactly what the role of the word “ensuring” is (although it’s probably a present participle). You need to include the full sentence (at the very least), and also copy the words accurately. Here are the problems: 1. There is no independent clause, therefore, it’s not a sentence. 2. “Package” is a countable noun, so it either needs a determiner (for example, an article, demonstrative, possessive) or it needs to be in plural. 3. “Essential” is an adjective, so it needs a noun to modify. Alternatively, this particular word can work as a noun in the plural. Include the full sentence (at least), making sure to copy everything accurately, and maybe someone will come along and answer your question.

Because in English, one sentence can only have one TRUE verb. If there was no -ing here, there would be two TRUE verbs in this sentence. “Ensure + ing” is a participle，not as verb but as adjoint adverbial in this sentence.

What is your question? I'm not following.

In English, we can often change an adjective clause to a participle phrase. So, for example, “The Korean government is sending care packages to people who are in quarantine due to exposure, which ensures they don’t need to leave the house for essentials” becomes “The Korean government is sending care packages to people who are in quarantine due to exposure, ensuring they don’t need to leave the house for essentials.”