I am looking for a better pattern for working with a list of elements which each need processed and then depending on the outcome are removed from
Select the elements you do want rather than trying to remove the elements you don't want. This is so much easier (and generally more efficient too) than removing elements.
var newSequence = (from el in list
where el.Something || el.AnotherThing < 0
select el);
I wanted to post this as a comment in response to the comment left by Michael Dillon below, but it's too long and probably useful to have in my answer anyway:
Personally, I'd never remove items one-by-one, if you do need removal, then call RemoveAll which takes a predicate and only rearranges the internal array once, whereas Remove does an Array.Copy operation for every element you remove. RemoveAll is vastly more efficient.
And when you're backwards iterating over a list, you already have the index of the element you want to remove, so it would be far more efficient to call RemoveAt, because Remove first does a traversal of the list to find the index of the element you're trying to remove, but you already know that index.
So all in all, I don't see any reason to ever call Remove in a for-loop. And ideally, if it is at all possible, use the above code to stream elements from the list as needed so no second data structure has to be created at all.