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I mean I could imagine some contract where party A agreed to continue to accept/transport/"deal with" all the oil party B produces, and is required to continue even if they are losing money on the deal.

I'm not sure why anyone would have signed such a contract, which is why I called it weird, but it does seem plausible.

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If you buy a futures contract, you are required to accept delivery of some fixed amount. You don't have to take "all the oil party B produces", just what you agreed to ahead of time. This protects you from upward price trends, and the producer from downward price trends.

Sure, but if the cost of short term futures contracts is negative or zero the oil companies would just buy them back instead of continuing to produce. When we say the cost of oil, we really mean the cost of short term oil futures.

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