It depends on the encryption mechanism, most ciphers these days are "block" ciphers. They work on independent "blocks" of data which are individually encrypted.
To encrypt, you need a key, and your plaintext, but you also need a random (but shared with the decryptor) initialization vector (IV) which pre-randomises the cipher, to help protect "replay" attacks, where the same message will always encrypt to the same value.
Simply using the same IV for each block is simple, but degrades security, as if your document contains lots of repeated data blocks, the encrypted copy will contain repeated data blocks in the same place.
A very popular way of encrypting documents has been to use cipher block chaining (CBC). The first block is encrypted with the shared IV. Then a hash of the block and the previous IV is used as the IV for the next block. This improves security, but has the disadvantage, that blocks must be decrypted in order. If a block is corrupted, all other blocks following will also be corrupted, because the IV that gets chained onto the following block will be junk.
An alternative method, and one that is used for full disk encryption is called Galois Counter Mode (GCM). In this case, the IV used for each encryption block depends on the original IV and the number of the block which are hashed together using a special Galois field hash algorithm.
The advantage of GCM in your case, is that as long your corruption doesn't lead to missing bytes (so that the block counter stays in sync), GCM will only produce corrupted output in the same blocks which were corrupted on the input.
GCM is frequently used these days, as it can be parallelized onto multiple cores (CBC can't, as it is strictly in order), and is convenient for disk encryption (which is inherently random in order). GCM is so frequently used, in fact, that Sandy/Ivy bridge CPUs contain a special GCM instruction to accelerate the computation of this function.
Cliffs:
You need to operate your choice of encryption algorithm (e.g. AES) in GCM mode.