United doesn't sell tickets with open returns using this terminology, you simply buy a refundable ticket which allows you to change the return date without penalty. However, be aware that refundable tickets can be several times more expensive that inflexible ones.

If he's planning to change the return date at most once, the optimal solution would be to buy a cheap fare which allows changes for a fee (keep in mind some cheap fares don't allow changes at all, so double check this before buying). The cheap fare plus the change fee will still be much cheaper than buying a refundable fare outright.

Thing are really more complicated than that because he will have to pay not just the change fee but also the fare difference in case his original booking class is sold out. However, if he has some flexibility in the return date and can make the change some time in advance, it will still usually come out cheaper than buying a fully refundable fare.