The pronoun "them" has no antecedent so all the answer choices except A are eliminated.

Hello!
Thank you for your question.

For this example, we're dealing with a non-essential phrase that I will put in bold for you:

For people who have never worked for a living, any job may instill a valuable sense of self-worth and open doors to better jobs in the future.

A non-essential clause means just that - it's not essential for the sentence to be complete. While it adds more detail, the sentence still should be able to stand on its own without it. Whenever dealing with non-essential clauses, read each option without that phrase in it, and see which one works the best. Let's do that, and I'll show you why A is the best answer:

(A) Any job may instill a valuable sense of self-worth and open doors to better jobs in the future.
A is correct because it can stand alone written this way, and isn't unclear at all.

(B) Any job might instill for them a valuable sense of self- worth and to open doors to better jobs in the future.
B is wrong because it includes the phrase "for them," but doesn't tell us what or who that's referring to. Even if you add that original phrase back in, it's still not correct to put this phrase in the sentence. It's unclear if you're talking about people who never worked for a living or some other group. It also shouldn't have the work "to" in front of "open" either.

(C) Any job may, in them, instill a valuable sense of self-worth, opening their doors to better jobs in the future.
Again, C is wrong because it refers to "in them" without saying who they are. Also, "opening their doors to better jobs..." doesn't make sense - it sounds like the writer is talking about actual doors that need opened, not an idiom as it's intended to be.

(D) Any job opening the door later for a better job and giving them a valuable sense of self-worth now.
This one also refers to "them" without saying who they are. It's also wrong because it uses the gerunds "opening" and "giving" incorrectly, turning this into one long sentence fragment.

(E) Any job may open the door for a better job later and giving them a valuable sense now of their self-worth.
E is wrong because of the same main reason B, C, and D are wrong. It uses the word "them" without clearly defining who they are.

I hope this helps! I'm available if you'd like any follow up.