My listening understanding is poor, but I frequently and clearly hear the word werden used at the end of sentences. What grammatical structure allows this and what is its function in this position?
As peterh pointed out in his comment, werden is frequently used in passive constructions:
Das Problem kann gelöst werden. (peterh)
[X] + [kann / könnte / sollte...] + [Verb im Perfekt] + [werden].
Another option are subordinate clauses (Nebensätze), where the word order is changed compared to main clauses:
Ich frage mich, ob die Briefe heute noch ankommen werden.
In this case, werden is not actually an infinitive, but is the inflected form (third person plural; but the same applies for the the first person plural) of the same verb werden. Its function here is to set the sentence in future tense.
Werden has many uses in the German language, as you can see in this overview with explanations at canoo.net.
werden has basically 3 meanings in German:
- "to become something". It is not in infinitive, but in first and third person plural (and in the polite-form "sie") it looks so: "Die Schüler werden Programmierer" means: "The studends become (...are becoming) programmers".
- Hilfsverb for Passive. Here the important thing is to know: what is coming with "is + perfekt" on English, is going with "werden + perfekt" in German. Thus, "It is done" means "Es wird erledigt". Here the "werden" is not in infinitive-form, but as in the previous point, sometimes it looks the same.
- Hilfsverb for future. It is the same as the English "will" hilfsverb, except that here the original Verb goes to the end of the sentence. For example: "I will learn more German" means: "Ich werde mehr Deutsch lernen".
You will most likely find (1) and (2).
Now, here werden is mostly not in infinitive-form and not at the end of the sentence. The most likely reasons, why it could become infinitive form:
- "we will", "they will", "You will" are all "werden". It looks like an infinitive, but it is not.
- If it is part of a vorgangspassive structure, and it has got a hilfsverb. Like: "Das Hotel kann aufgebaut werden."
The most likely reasons, why it can go to the end of the sentence:
- It is part of a subordinate clause (Nebensatz). In German, there Verbs are going to the end of the sentence.
- Like (5).
You can freely combine these possibilities, to find your best variant.
These all are looking chaotic, because you clearly don't know the grammatik of the German verbs. But, in fact these are simple and very logic. Because the whole German Language is very logic.
If you have a programmers vein: you essentially asked: "How can this function result 5?". To describe, how can a function result 5, might be complex. But not if you understand, how the function works.