It's gone. You cannot save data without having space for the data. If the luggage compartment of your car is full, you cannot add another suitcase either.
Unfortunately, OBS doesn't check if the disk gets full, so you have to make sure you have enough space available.
But I would not run my computer at the edge of being full - today, storage space is so cheap, it's a bad idea to not buy this little convenience and get some multi-TB sized disk that never gets full. And it's not a good idea to buy a computer with only 1 TB disk space in the first place if you have video recording in mind.