I was confused by a company slogan I saw, and that made me wonder: Is it correct to write "a dream come true"?
If I was the one writing it I would use "a dream comes true" but is the initial form wrong?
It is correct. Come is a past participle here, not a simple present. It means a dream [that has/is] come true. The past participle come can be used with the verb be, which is why a dream come true is possible; this is normally possible with all verbs that can be or once could be used with be.
a horse [that was] left behind
a day [that has/is] gone by
"A dream come true" "Come" is the past participle form of the Irregular verb "come". It is in a verb form but used as participle modifier of the word "dream". A participle modifier is a verb form but used as a modifier or an adjective. So, the word "come" describes or tells something about the word "dream". It's just like saying " A project done well".
A dream come true- a dream that has come true A project done well- a project that has done well or a project that is done well.