***** NOT A TEACHER *****
Hello, yamyam:
May I add my two cents' worth to the teachers' excellent answers?
As we non-teachers must do before posting, I have checked my books and the Web before posting this. So I think it is
accurate.
(1) "come true" seems to be a fixed expression/phrase. The word "come" does NOT change tense.
(a) Look at this sentence from Merriam-Webster's Learner's Dictionary (Web):
"The trip abroad was a dream come true." (Although the trip was in the past, you do NOT change the verb to "came.")
(2) Mesdames Anne Paxton and Meryl Wilkins in their Teaching Adult ESOL (Google books) say that "come true"
is a fixed exoression (you do not change the tense). They tell us that it usually collocates (combines) with "wish"
or "dream." It does not collocate with "problem."
(3) Be careful! Look at this:
I will be 76 years old come March, 2013. (If I live that long!)
(a) The use of "come" here is different. The books (such as the great Professor George Oliver Curme's masterpiece
A Grammar of the English Language) tell us that we are dealing here with something called the subjunctive. It is an
elegant way to say: I will be 76 years when March shall come.
(i) I think that in regular English, people just say: I will be 76 years old next March. If you want to sound quite
elegant, you could say "I will be 76 come March," and if you want to be super elegant, you could say "I wll be 76
when March shall come." Of course, in 2012, nobody would use the last sentence. But people definitely use the
second sentence. Here are some real examples that I have collected over the years:
"The Report," which come September will air on Channel 4."
"Our plans will be settled come Friday."
(4) Returning to your original question, "come true" does not change in "His rise in the company is an American
dream come true" because it is simply a fixed phrase/expression. It means (as the Learner's Dictionary says):
"to become real: to happen in the way that you wish or dream."
HAVE A NICE DAY! (Thanks a lot for your question. I learned a lot.)