In general, you cannot encode information such that "any variance at all in the inputs causes the decoded secret to be completely useless." That's because there's a generic attack that can be used to reconstruct the secret with a high probability, given almost enough enough information to uniquely determine it, as long as the correct secret can somehow be distinguished from incorrectly reconstructed secrets.
The attack is simple: you guess the missing information, reconstruct the secret based on your guess, and repeat this for all possible (or at least all sufficiently likely) values of the missing information. Then you compare the resulting secrets and pick the one that appears to be the correct one.
For example, let's say that the secret is a password shared using a threshold secret sharing scheme (like Shamir's) using threshold $t$, and that we know $t-1$ full shares plus all but the third byte of the $t$-th share. Now, there are 256 possible values the missing byte could have, so we can just reconstruct the secret using each of those values, giving us 255 different passwords.
Now, depending on the details of the secret sharing method used, we might be able to guess which of these was the correct password just by inspection; for example, if 255 of the reconstructions looked like random noise, while only one consisted of printable characters, we might well guess that this was the correct reconstruction. However, in this case, we'd have an even more reliable way to tell the correct password from the incorrect ones — we could just try each password and see which one lets us decrypt the data or log in or do whatever the password is supposed to be used for.
The same attack can be applied to other kinds of missing or corrupted information, as long as we have some idea of what the missing information might be. For example, if each share was $n$ bytes long, and we only knew (or suspected) that some byte of some share was wrong, we could just try changing each byte of each share to each of its 255 possible alternative values, giving us $t$ × $n$ × 255 reconstructions to choose from. For typical values of $t$ and $n$, this should still be easily manageable.