I think I've done this once or twice in a Gardens game.
Edit: This was a fun turn:
Previous clean-up:
(Davio draws: a Copper, a Province, an Upgrade, a Gold, and a Silver.)
— Your turn 18 —
You play an Upgrade.
... You draw a Silver and get +1 action.
... You trash a Province.
... You gain nothing.
You play a Copper, a Gold, and 2 Silvers.
You buy a Province.
(You reshuffle.)
So I trashed a Province for nothing, because I had exactly $8 for the last one.