How can stepfather adopt if father terminated rights in Illinois?

You need legal counsel for this one. You should have no problem at all since the biological father terminated his rights as the father of that child. Do it legal so there is no chance of further trouble from the biological father. Termination of rights to his child doesn't mean much if he lets a few years slip by and can convince a judge that he was too young at the time, but has now matured and would like to be part of his child's life. A judge may very well grant him his wish and it's trouble for you!