Collateral on Aave still earns interest?

Hi all,

On many platforms like Celsius, if you want to borrow against your collateral, your collateral won't earn interest anymore.

But I heard the other day that your collateral does earn interest on Aave. Is it true? I read the docs and nowhere did it say that the collateral does NOT earn interest, so maybe it does earn interest?

If it does, why would Aave allow this? They need my collateral in case whatever I borrowed goes down in value. So if they pay me on my collateral, they would need to somehow make money off of my collateral as well, which means they would be rehypothecating? I would imagine Aave doesn't rehypothecate…

Any help appreciated,

QAR