This is really two fairly independent questions - when do you want to keep a copper rather than net +2 coin and when would you play a dead action. We've done these puzzles to death and here are few highlights:
1. Diversity. There are several reasons to keep your last copper to increase deck diversity - Fairgrounds, Menage odds, Hunting party stack making only 7 next turn, Horn of plenty needing activation with the copper.
2. Card count. Gardens. Pstone. Madman deck (dropping deck size limits how much you can draw from your final few Madmen if you are doing crazy things like Kc x3 -> Upgrade (Fortress -> Cache) x3 -> Madman).
3. Copper has intrinsic value. Apothecary. Bank. Coppersmith. Counting house (you got the Moneylender after he swindled a potion into it). Fine tuned engine that won't hit 8 next turn. 7 Venture deck.
4. You want to top deck it. Keep Loan from discarding a Plat (need to play Loan for other reasons), want to go Mandarin -> Ironmonger, have other top decking (e.g. Alchemist) that will leave copper on top (e.g. Thief/Swindler/Jester defense). Possession defense.
5. You want to trash the copper with something else or later in the game/turn. Altar. Upgrade in a Highway game. Mine. Have a Market square later in deck you want in hand first.
6. Need something to gift with Masq.
7. You care about handsize. Madman. Cellar. Storeroom. Hamlet activation. Vault/Secret Chamber (e.g. using Chou to draw lots of copper, Cellar to draw everything else, Festival for actions & buys, and Vault for cash).
Why would you play a useless action?
1. You have to - Golem, Throne Room.
2. You want to get rid of it with Procession.
3. Peddler cost.
4. Conspirator activation.
5. Horn of plenty activation.
6. Reducing hand size for limited draw; reducing duplicates for Menage.
7. Removing the card from a reshuffle triggered mid-turn (e.g. Minion).
8. Allowing Shanty town to draw.
Pretty much you can mix and match between these two lists. Pick a reason you really want to play a dead & useless action. Pick a reason why you want to keep copper, then make the needed assumptions about which cards to draw to make the two line up.