You could include the word “them” and say “If it’s possible to ask them why they joined….” It’s not really necessary, though, given the context. The reason you can’t use “that” with “why” is because “why” includes “that.” In introducing a subordinate clause, “why” = “the reason that,” so you could say “… ask (them) the reason that they joined….” To tell the truth, “that” is still optional, and I would omit “that,” saying “… ask (them) the reason they joined.” The same rules apply to the other question words used to introduce a relative clause — they imply an unstated “that.”

"They" is the correct answer, not "Them" This is because "They" is used to describe people doing something, just like "Them", EXCEPT that "they" is said before you say action and "them" is only used after you say the action. Let me explain: "They" always is said before the action (no matter what it is). "They are running. They do not know anything. They need help. They would do it. They like to read." "Them" is always used after the action is said. "The people who were running was them. The ones who do not know anything is them. The people who need help is them. The ones who did did it is them. The people who like to read is them." Notice how I have to tell you "who" is doing "what" more than once. I have to use the noun "The ones" or "the people" and then I have to say "them" at the end. "it was them. "it" is the the noun and then I say "them". If you used "them in your sentence you would have to explain yourself more to use the word "them" correctly. "Why the ones who joined the group beating was them." That is too long, even though it is correct. To make it more simple we use the word "they" to get our point across faster. "Why they joined the group beating." I hope this answered your question. I know English can be confusing. Good luck with your studies. Feel fee to ask for help any time.