come out of is just as apt as come out from

Unfortunately the program does not allow for many of those alternative translations to English. It also seems strange to me that this translation for BESÉTÁLNAK is "they walk into", but VADÁSNAK is "hunt" without the "they". Of course, translation to English that leaves THEY out of "they walk into" is wrong and inserting "they" before "hunt" is also wrong.

Exactly. English seldom requires that the pronoun be repeated in this type of sentence, and quiet often it is not necessary at all. Since we know there are BEARS involved, we know THEY do everything in this sentence.