I have been looking for something that probably doesn't exist for
reasons I don't know.

I am trying to find out if there is such a thing as a heat exchanger
for a dryer that would attach like a humidifier to a furnace?

I have read MANY posts and articles about just piping the exhaust of
the dryer into the house and how bad that is with lint and moisture.

What I am looking at is something like an air-air exchanger where each
"circuit" is closed.

So the dryer would still exhaust outside but on the way it would flow
through a box that is on the cold air return of a furnace. The
furnace would suck air through the box and collect some of the heat.

Just curious if anyone has ever seen anything like this, if it is even
feasible, and what issues this would cause?