Posit the following situation: A wizard has True Polymorphed a stick into, say, an adult Silver Dragon, and maintained it for the full hour. He uses the thing as a mount, he's kept it happy with the idea, and all is well with the world. An enemy catches them both in an antimagic field, and while he's picking himself up off the ground, breaks the stick in half and hands the two halves to two goblins, who start running in opposite directions. What happens when the goblins in question clear the antimagic field?
The original object ceases to be a valid target for the spell and the True Polymorph fails or is suppressed, depending on what the DM decides
From a previously answered question we know the target of the spell remains the target of the spell for it's full duration.
In this case, what has happened is that since the stick is broken the target has permanently become an invalid target for the spell (it's now two objects instead of one). In particular, neither sub-portion of the stick is the target of the spell, and thus the spell cannot become "un-suppressed" on either of the two halves of the stick.
You are essentially asking a more general version of Is a spell suppressed or removed when the target temporarily becomes invalid?.
According to the accepted answer in that question, Jeremy Crawford has tweeted that:
There's no rule governing what happens when a valid spell target temporarily becomes an invalid target. A good rule of thumb is that the spell is suppressed while the target is invalid.
So...it's up to the DM!
However, if the target is permanently invalid, there isn't a hugely practical difference between the spell fizzling (ie it is effectively dispelled) and the spell being permanently suppressed...barring maybe the wizard attempting to mend the stick post battle.