Jay is basically correct. Here, "come to life" is a past participle. It's a verb phrase that is working as an adjective. It's much more common to see *passive* past participles, like in these examples: "That was the story told by our ancestors." "These are the products received by our company." "This is the book written by my teacher." Active past participles are more rare, so it's hard to think of many good examples, but the basic idea is the same. "Come to life" means "having come to life" or "that has come to life," and describes the fairy tale. You could also say: "He's like a man returned from the dead." (He's like a man [who has] returned from the dead.)

Excellent answer by Gray. I will bookmark this one.

I suspect it's because it's older English and it's just the way "come" is said in the past tense rather than using the word "came" like we do now. We don't question it, we just say it that way because it's a set phrase. I would also say that this form of the expression only applies to personified but non-human objects. For example "a fairy tale, vampire, zombie, statue (etc) come to life" but we would never say that for a person even if resurrected (if you believe that sort of thing).

This is a really good question! Luckily, I have an answer. The reason is because this is a shortened form of "a fairy that has come to life." So this subordinate verb phrase's verb is past rather than present. I hope that helps!