DH wants to adopt but he is afraid of drug effects...

Hi all, We've decided to start the adoption process. DH is a little concerned on regards the drug stuff....I lnow agencies do test the birthmother for heavy drugs...can you please give me any advice in how to go through this fact? If the mother lied about not using drugs and the baby is born with drug effects can the adoption be revoked? I know that this doesn't matter since we would love the child but we can't aford a child with known severe medical needs.. Thanks a lot