An animal that is certainly doing that today is the raccoon. Raccoons are regarded by many as a nuisance, but, particularly in urban areas, they have taken to raiding human garbage. This may be the initial stage of domestication. In due course they will proceed to the inside of the house and sympathetic humans will feed them - maybe.
However, before you go rushing out to obtain a raccoon as a pet, you should be warned that in areas of the United States it is illegal to keep them in captivity. They are also susceptible to rabies. While occasional raccoons have been kept as pets in the past, I think it is a long time until - if ever - they become commonplace in the home.
Below you see a picture of a raccoon and a skunk happily sharing human refuse. Is this truly the first step to domestication?