Can I negotiate missing the last connecting flight on a journey with an airline and still use the return ticket?

As you've not yet booked the flight, you have an easier option than negotiating - booking an Open Jaw (sometimes called Multi-City) ticket.

On Finnair's website, this is hidden away on the book flights tab under "Other Options", (next to Stopover). For some random dates in April, it's pricing up for me in economy at $623, although that's entirely on BA flights, and via London rather than via Chicago and Helsinki.

You don't need to enter each individual airport you're flying through - just the first and last of each separate journey. Assuming you don't want to stop for a while in Chicago, your first flight is Denver to Helsinki, and your second flight Stockholm to Denver.

If flying with Oneworld airlines isn't important, you can perform a similar search with Google Flights to get prices across more airlines.

What exactly is a open-jaw flight? has a lot more detail on what exactly an open jaw flight is and how the airlines work out the price, and Is there a flight search engine that allows me to pick the departure and return flight separately? gives a touch more detail on how to book.

"Can you negotiate...with an airline?"

NO. **

What you can do is build an Open Jaw/Multi-Stop itinerary. It will probably price out very close (maybe less, maybe more) than the Round Trip. There really is no negotiation involved, these itineraries are very common.

**For the nitpickers, yes, you can, but a single passenger is not something commercial carriers would entertain.

Your "negotiation" is what's normally called "changing your ticket." And if you call up and ask to do this, you will likely be charged the difference in fare plus the applicable change fee for your reservation. This could prove quite expensive, likely more than if you just booked the itinerary you want in the first place. They do this to protect their pricing for flights to different markets; otherwise everyone would just book a flight to a cheaper city and request to change it later.

It is possible that a reasonably flexible airline would work with you and at least waive a change fee if you had a very good reason (car accident on the way to the airport, hospitalization, etc... with proof), but this is more of a customer service accommodation than something you can rely on, and it would not apply in the situation where you simply prefer other plans for your vacation.

I would try pricing out Denver -> Helsinki with a return of Stockholm -> Denver on various airlines. While some airlines have increased fares on multi-city trips lately, it's not always more expensive, especially to add an open segment within Europe, and you may find that you get exactly what you're looking for.

Others have addressed your answer perfectly but for those who come by Google search, I wish to add that if you have already bought the ticket, you can't leave the last connection out without invalidating the return ticket (and without negotiating for the change).

The practice of using only a part of the connection fights - apparently usually missing the last connection flight - is called "hidden city", and it is often practised, but in the case of return flight it would invalidate the return flight. Source:

http://www.huffingtonpost.com/barry-choi/why-hidden-city-ticketing_b_7883384.html