It's my understanding you can adopt an adult but it will not change his/her immigration status. They won't qualify for the same rights as a minor adoptee. Speak with an immigration lawyer and an adoption lawyer because it involves 2 different situations really.
People can be adopted only under the laws of their country of citizenship. For instance, a USA person can only adopt a Chinese adult if Chinese law allows it. (Which it does not.) And adopting a person over the age of 16 will not have any impact to the person's visa status. US law allows for an adoption visa to be granted to children under 16, but not to those over 16. And there is no other type of visa that allows their status to be changed solely on the basis of having been adopted.
Be very careful when you or the adult in question discusses this issue in a public forum. It could appear as if the individual got a temporary visa with the intent of staying in the U.S. permanently, which could be construed by the USCIS as intent to commit visa fraud, a felony under federal law. It could get the person's temporary visa revoked, and could cause him/her to have to return to his/her homeland and never come back to the U.S. Sharon