Nitpicky comment - at the very least, it needs to be action-duration
The idea seems sound. Some thing that you play once, and then keeps trashing one card every turn until it doesn't.
Useful for trashing coppers - you have one turn early where this uses up a slot in your hand, and then probably for 3-5 turns you'll have a copper to trash with it, and you still get the value of the copper, until you get unlucky and don't draw a copper to play with it. Can't trash estates. It's faster at trashing coppers than Moneylender, but gives you no benefit.
I have no idea whether it's balanced - that has to be playtested. It's obviously not good for any BM+X strategy, but I'd definitely buy it if it was the only trasher around and I wanted to set up some sort of engine. And there was no cursing, since it can't trash curses.
Possible ways to make it more powerful while staying thematic:
1) On the turn when you discard it from play, optionally let it trash a card from your hand.
2) Have it accumulate tokens for each card you trash, and then when it gets discarded, give you some benefit based on those tokens. (Gain a card worth up to X? After you've used it to trash six coppers, you can have it gain you a gold?)
3) Give it a reaction-like power - maybe let you discard it from play to trash a card that you're about to gain? Then you could have it keep trashing coppers until someone gives you a curse, which you could then block. This would be a really powerful, though.
4) Let you trash it from play instead of just discarding from play, for one of the above benefits.
5) Maybe have it give you some benefit on the turn you discard it from play? It would be trivial to make this a $4 card, I think, by basically making it a terminal silver; something like "you may choose to get $+2. If you do, you must discard this from play at the end of this turn". (You'd have to make the wording work.) Or give a more interesting benefit than that.
Unfortunately, a card that stays in play permanently is different enough from anything we've had so far, that I don't really trust my intuition about how it would play out.
Try playtesting it as compared to Moneylender. Set up an engine board and have one person open with one of these and the other person open with Moneylender and see how it plays out when you pick otherwise similar strategies.