Publication fee will not be paid at deadline – what will happen and how should I proceed?
Definitely contact the publisher about this. This is a publisher-level question, and likely not something the editorial board will be able to handle.

The good news is that the publisher is almost as interested as you are in getting the paper published. They (or the editorial board) have already put in the effort to get it peer reviewed, and from your description, they've likely also put in the effort to copyedit/typeset/get a DOI/etc. They have little to gain by not publishing the paper, and while putting a paper online for free is not ideal, there's something to be said for building goodwill as well.

I suspect the most likely result is that they'll hold off on Open Access. In other words, your paper will be available to subscribers only. If this isn't possible (the journal is open access only), they might delay publication until the payment is received. If the payment is never going to come, they might publish anyway but hold on to the copyright (free access, not open access), or provide a heavy discount or even just give free OA. For example, if the editorial board tells the publisher your paper is really good, they might be more inclined to give free OA.