At secondary school I was dealing with Agat computers at school computer class (exactly, this was Agat-7), approximate clones of Apple II series. Their 5″ diskette drives were also clone of 140kB drives designed by Steve Wozniak and Shugart for Apple II, with hardware adjusted to what could be produced in the socialism camp. One may find a deeply detailed description of the drive here. There were some weird design choices, as the absense of an zero track sensor. To seek to the zero track (after reset or I/O error), it unconditionally performed 160 steps of the head position stepper motor. This caused gradual disbalancing of the head positioner through regular impacts into seeking limiter (with a loud, machinegun-like burst sound). As result, at my final class at the school, the computer lab consisted of 3 groups of 3 computers each, where one computer can easily read diskettes written by another computer in the same group, but struggled with diskettes from other groups. And, this issue was known throughout the entire Agat park.
To solve the readability problem, a program called COPYTREK was developed (by a Moscow firm associated with the factory that produced these computers) to recover unreadable diskettes. It tried to read all sectors of a track in the following manner:
- It applied brief affections to the stepper motor to make it turn to an angle less than a single step, positioning the read-write magnetic head at offsets like "1/8 of the track interval", or kept two neighbor phases turned on to position the head just between them. A sector was being read multiple times with different head offsets, to find a best reading result.
- Besides (1), multiple readings were applied to find unstable bits and statistically determine a most probable variant.
There were no algorithmic recovering due to lack of redundant bytes (as most current drives utilize Reed-Solomon or similar methods), only a single XOR CRC byte, but this was enough in most cases. After reading, user could command the program to write a track back to diskette, according to the current drive "tuning". (It would ask if you wanted to replace the diskette with a target one, if you preferred to preserve the original.)
All this weird magic was specific to so-called 140kB Shugart drive (35 tracks of 16 sectors of 256 bytes). Just after my graduation from the school (1990), it had got a few computers of a new model, with 840kB drive that was saved of this issue due to adding of zero track sensor. (But this was time of a speedy decline of Agat usage due to import of MSX and IBM PC series.)
I hope this will answer your question, despite this was not PC specific.