If the government decided to make Social Security a private corporation it could. If it did this, keeping in place Social Security “taxes” that would then go to the new corporation, we would not consider Social Security a budget expense. Being government owned or private doesn’t matter in terms of how the expenditures should be considered. This is why Social Security and Medicare are not part of the normal budget negotiations at budget time. These are obligations that need to be paid to the people who paid for them.