I've seen drives handle bad sectors by themselves perhaps on 1% of the occasions that I've seen dodgy disk problems.
If you see any symptoms of anything wrong, the drive is already failing, and it's time for data recovery procedures. HDDs come with bad sectors already re-mapped, and if any develop over time, they remap those. You can check SMART data to see how often this has happened (often 0). As drives have become denser, it has become acceptable--per the manufacturers' ideas of the world, anyway--for some number of sectors to need remapping over the drive's life.
The drive will automatically remap a bad sector to a reserved sector. That doesn't always mean that it can read the sector. if it can, it will move it, and no data will be lost. If not, it hopes that you write to that sector, instead of read, next time, so that it won't have to fail on you. But, it is generally acceptable (as in what's on the spec sheets) for an uncorrectable read to occur somewhere around 1 sector read in every ~12TB, for consumer drives, IIRC. Actual stats of healthy drives are much better than that, of course, every time anyone has measured them (the spec sheets are worst-case).