Adoption

The Catholic Church operates more orphanages (BY FAR!) than any other church or orginization; there are entire Religious Orders devoted exclusively to this ministry, and in some countries the ONLY orphanages are those operated by Catholics. So I think it's pretty safe to say that the Catholic Church strongly encourages, promotes, and facilitates placement of orphan children in good homes.

But I don't know what you mean by "adoption of parents." Do you mean something like taking an elderly person (unrelated to you) into your home and caring for him/her, becoming legally responsible for that person? I'm not sure I've ever heard of such a thing, at least being promoted on any large scale. And I don't think such an arrangement has legal standing under US law (though it might essentially be accomplished through power of attorney, but not by "adoption." PoA is revokable, however, whereas adoption is not). I think the Catholic Church would support such an arrangement, though I don't think She actively promotes it (not in the US, anyway).