Can we look just at the other features when we have a missing vaue?
Try a few options and pick the best.


Fill in the mean/median from known $c$'s in the $a,b,c$ model
Create a linear regression model to predict $c$ from $a,b$, fill the estimate $c$ from this model in the $a,b,c$ model
Train both models and use the applicable one


Personally, I think 2. will work best in most cases, but 1. can already be sufficient when $c$ is not correlated to $a$ or $b$.