I think that "too small for them to live in" suggests that the space is too small to live in comfortably, where as "too small for them to live might infer that they will simply die for lack of space. : )

"Live in" can also refer to a person who lives in the same household as the subject of the sentence. For example; "live-in made" or "live-in girlfriend" but this is usually hyphenated, and usually only to clarify when it's possibly ambiguous whether the related party does in fact share a dwelling with the subject. This is a rare usage but you may here or read it from time to time. Also note we do not use "live-in friend" but rather roommate.

Hi Kyouko, You are referring to a phrasal verb. By itself, the word "live" may mean to harbour life, or have the quality of being alive. However, when an adverb or preposition is paired with the verb "live", the meaning changes. We "live in" a home, a city, a country or even a planet. The preposition "in" indicates the placement of something within a certain space. Hence, "live in" means the place where you reside. Hope this helps. Cheers, Lance

"Live in" refers to structures and locations specifically - "I live in New York City. I live in an apartment. I wish to live in a house in Tokyo." English is glued together with these prepositions (https://en.oxforddictionaries.com/grammar/prepositions) to show relationships. "Live" on its own is more abstract and about existence generally. "I'm living well" means "I am healthy. I am happy." This is also seen in the phrase "to make a living", which refers to job or occupation - "I make a living as a teacher."

You live in the house, in the apartment etc. so when you refer to a place you literally live in, you should add "in" at the end, otherwise it sounds like Christopher explained to you; It is very common in English to leave "for", "at", "in" at the end of the sentence, f.e. What are you waiting for? What are you looking at? Where would you like to live in? - the last one suggest what type of house/building do you prefer. (vs. Where would you like to live? which refers to a country, a city etc.)