When using failure rather than fails, it sounds more natural to drop the subject and verb in the first clause:
After a failure, the printer will return error message 1.
You can mention also mention a specific issue:
After a paper feed failure, the printer will return error message 1.
(Note that from a technical perspective, generically failing to print documents correctly isn't something that can really be linked to a specific error message. Not printing correctly could be caused by any number of things: the printer could be out of ink, it could be jammed, there might not be any paper in the tray, and so on. Each specific reason for a failure to print correctly would likely result in a different error message.)
But you can also use your original construction, although I find it a little awkward:
After a failure that results in incorrect documents, the printer will return error message 1.
Generally speaking, it doesn't sound quite right for something to encounter (or have, or suffer from) a failure. Instead, we would normally say that there is a failure.
If I were to choose between the verbs, I would probably use encounter:
When the printer encounters a failure to print documents correctly, it will return error message 1.
But there's nothing wrong with the other verbs either.
However, my advice would be to keep the original formulation, or drop the reference to the printer in the first part of the sentence and just mention the failure itself.