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Not that this helps at the moment, but I understand there is a POS device which uses cellular as a backup. It might be a consideration if loss of data is likely to recur.
The ADSL internet cutting off 2 weeks after fibre was supposed to be switched on sounds exactly right (Telus is assuming the fibre was installed as planned). The normal operation is that when you have business internet service they give you 2 weeks of simultaneous service on the old adsl line so you can test and switch over on your own schedule (As many companies do not want to take the time to do this in the middle of a work day while fibre is being installed). Often a business needs a bit of time to switch especially if they have static IP with VPN's or services pointing to the old IP. This actually is a good reminder for myself as I have a client where something like this happened last week and the fibre install hit a snag where they need to come back to finish. I should call to make sure their old service will not be removed accidently.
So yes, if they could not complete your internet install and your internet on the old ADSL line is cut off that sounds like it happened exactly as you describe. They forgot to cancel the removal order on the old service and they left the fibre install order open and will complete it when whatever problem your installer ran into is resolved up the line. So the installer likely didn't anticipate this situation, and probably doesn't have any direct knowledge of the pending cancellation order in the system for the old service. It's likely something they rarely see so there is no procedure to catch it.
So yes it sucks. But they have a solution for you when your internet is down for any generic cause but you needed to be proactive about it. They offer an add on to your internet plan where they give you a cell phone hotspot device with an ethernet jack (Called 4G wireless backup) which you can plug in during an outage to get online in an emergency while waiting for technician to come to fix. I believe there is a limit of 1Gig of data usage but for typical point of sale terminals where it's only for card authorizations that is more data than you would ever need (not much if the store clerk uses the computer to watch netflix while waiting for a customer though). They usually offer this as part of their "freedom bundle" packages that bundle up internet, phone and sometimes wireless cell phone service on one bill. Last time I inquired it was $10 per month and the hardware was either $150 with 2yr contract or $300 for the 4G smart hub device. The plan only worked in these smart hub devices (because I tried it in a tablet to see once).
This requires you to have already done a little planning on your part. Once the internet is down and you have no backup plan it's a little late. But having programmed a few of these point of sale terminals I know that most of the stand alone models can still be plugged into a regular phone line and switched back to dialup mode. Call your credit card processor support line for instructions to change the mode back to dialup and make sure you have a cable handy and know where the right phone jack is you can use. (Fax lines are the usual first choice)
If your internet is absolutely mission critical Telus also has guaranteed managed services where they give you a contract with specific maximum repair times they must meet to fix the problem until penalties kick in. These are much more expensive than standard "best effort" level internet services like yours. If you are making the claim that any time the internet is down you are losing thousands of dollars an hour/day then it could be worth it. Of course that might have been an exaggeration on your part but we will assume it could be true and managed services might make good business sense in that case.
So you should have at least 2 different options for your debit terminals. If it's just a stand alone card terminal you usually still have the option to plug it into a standard phone line and change your connection mode to dialup. If you get the instructions from your provider you can do it yourself and it takes about a minute to change the mode. Usually if you have done this before you do not need to set all the programming for phone numbers and merchant account numbers and such so only changing modes can be very easy and quick.
If you need Internet for more than just the debit machine (You use a cloud based service for point of sale software for example) then you should have a backup internet modem of some kind. Telus sells a wireless plan as an optional add on for their business adsl plans. You might consider paying for an account with their cable competitor. You may even be able to use a cell phone in hotspot mode if the computer has wifi or you can sometimes get a wifi bridge device to convert that hotspot connection back to regular old ethernet eg: Asus RP-AC56 and use the cellular account you likely already pay for. Point is there are other options that you can take on your own. I know it sucks and you came to vent. For the most part we are all just customers too, but there are solutions that do not involve throwing your hands up and declaring defeat.
And I'm putting a note in my calendar to call Telus tomorrow to double check on that client of mine who had their fibre install delayed to make sure the same thign doesn't happen. If it did, then I have a backup solution similar to ones I describe in place but it's not ideal as any backup is usually a compromise.