The EU decided early in the process to use Ireland as a bargaining chip to pressure the UK. The idea was to allege that the UK had to guarantee no border in Ireland and
therefore*
grant a series of concessions in regulatory matters to the EU,
including submitting to present and future EU laws and courts. In practice it calls for the UK to abrogate its sovereignty to the EU. This was the "deal" the EU demanded from the UK. Either place NY under that "deal", a UK territory under EU law, or place itself (the whole UK) under that "deal".
Obviously no country places itself under the laws of another power lightly (to say the least). This was such an exorbitant demand that it was refused three times in parliament despite all the fear-mongering, and despite the fact that most MP are openly pro-EU.
It was made worse by the fact that this international treaty between the UK and the EU commit the UK to remain bound by it until the EU saw fit to release the UK (the "backstop": if no new deal was reached between the EU and the UK, the UK would remain a vassal of the EU, obedient to any future legislation it decided to produce, and to any court decisions it passed, on a wide range of subjects).
Without a deal, the nature of the border in Ireland is undefined. It may be a guarded border, or it may be a nearly nonexistent one. It depends entirely on how the UK, on its side, and Ireland, on the other side, decide to enforce it.
The UK's government can easily declare unilaterally that products and people can continue to cross the border freely, and do its custom checks on the ports that connect to Great Britain. Due to the lack of any infrastructure in the border this is its most logical position for the foreseeable future, a few years at the least. There are no downsides to the UK for doing just that: Ireland remains part of the UK fully and exclusively under UK law, its locals and products can be waved through any customs checks (with some fraud to be expected, but that's not a problem really), and the situation can be revised if necessary.
The sole reason the UK hasn't agreed to a "sea border" in a deal with the EU was that
the EU demanded more than this: it demanded that
EU law apply to Northern Ireland, and that this situation of legislation above the UK law and having a "sea border" be
permanent.
As for the position of the Republic of Ireland, it is complicated. The RoI would wish that no border existed, and be happy to reach a deal with the UK to move customs checks to ports. But the EU has been (so far) understood to demand more, that the RoI enforce a "hard border" across the island. The whole
excuse of the EU to demand that the UK accept a deal submitting itself to EU laws was the
story that without such a "deal" a hard border would be inevitable... can they change tune in the event of the UK leaving without submitting?
Imho they can and will, with little embarrassment, made easier by the fact that the whole commission and the godfather of the bureaucrats in Brussels are being replaced. And journalists will have a collective bout of amnesia about what had been demanded prior to the UK's exit without a deal, and just cover the "wonderful new solution" of doing customs checks over the Irish Sea.