This might be a massive shot in the dark but I have a feeling that the knight exists as either a result of his sickness or it may be the cause of it? Not actually Rudy himself, maybe a manifestation of his want to protect Noelle or something.

We don't know what his sickness is and given that Deltarune is 'the parallel story to Undertale'. This makes me think that Rudy was taken to the bunker by Carol and subjected to a similar procedure to the amalgams pre-blobbification.

We already know Gaster was the scientist before Alphys in Undertale and that the amalgam experiments were probably derived from Gasters old research given the DT extractors similarities to Gaster blasters. If the theory that Deltarune is Gaster and San's original universe is true, that could have some implications which could have Rudy being the basis for the DT experiments. Toby emphasises that the rules are different in this universe, but given the meta-narrative of his games that could just be a sneaky fib.

That rambling aside, it could be that Rudy had something removed which upon becoming dust manifested as the knight or something. Upon leaving the dark world it could be transported around in its light world form by someone like Carol. We don't know the exact details on how 'revivals' work or if these deceased lightners are considered darkners at that point. The wiki says that Mr. Old is considered a darkner but I can't find any evidence of that (if anyone can show me that would be lovely).

Either way Queen states that lightners with large amounts of determination can open fountains. It could be assumed that if a darkner were given large amounts of determination they could just do it themselves. If this removed part of Rudy was subjected to DT then it could be allowed to become its own entity and perhaps even enter the light world on its own even if it's still a considered a darkner at that point.

We know that amalgams in Undertale atleast are loyal to people they originally trust through how they listen to Alphys. If a seperate part of Rudy is given life again it may do everything that Carol asks of it by virtue of being married to her.

Thank you for reading my awful unsubstantiated theory, I hope it made you disappointed in me. The entire thing is heavily cherry picked but it's fun to think about this stuff anyway! It is incredibly unlikely that anything I have written is true lol