I get the sense that the OP is looking for what used to be commonly marketed as an "open-ended" ticket. I bought one to Europe on DL in 1995 or so at a very small premium above the lowest coach fare. Outbound was fixed, return was variable and required 72-hour advance notice and was I'm sure limited to some of the more restricted coach fare buckets. I want to say it was only $40-50 above fixing the return date. This was in an era when an international itinerary change fee was $100-150. I distinctly recall it being a better deal than just guessing at a date and being wrong. I really had *no clue* when I was returning, so it was a pretty safe $40-50 bet that any guess I made would be wrong.

I don't know if this exists anymore or not, although the OP's description of the Asiana fare in question suggests that they do. (Question: is that really the rock-bottom fare? Or are you paying some amount for the one-change privilege? If so, it is worth it compared to paying a change fee?)

Of course you can always buy a flexible Y fare, but I get the sense the OP already knows that. And the open-ended tickets back in the day were actually designed for this purpose and for a nonrefundable ticket buyer.