I'm really sorry for your loss. Our 12-year-old diabetic cat also had to be PTS earlier this year, as his blood glucose had become completely (and inexplicably) unstable.
Please reassure yourself and your neighbour that there's a strong chance it wasn't human error with the insulin. One common cause of hypoglycaemia is that diabetic cats can go into remission. Suddenly they don't need their insulin, but you have no way of knowing, so they get their normal shot and drop too low.
Our cat was previously a textbook-case diabetic, thriving for years on a high insulin dose. When he did have his first blood sugar crash, it came out of the blue, and I was paranoid that I'd messed up his shot. I'd started a new vial which had been in the fridge for a while, and I was worried I hadn't rolled it enough so he'd got a super concentrated dose.
But after the first hypo, he continued having sudden drops every few weeks. We went through 12 months of daily blood glucose monitoring, switching doses, switching insulin, additional meds. He'd be okay for a few weeks, then have another sudden plunge. The vet never worked out what exactly was causing this: it wasn't remission, because he still needed his insulin... except on days he didn't (and even if his blood glucose was crazy high when I gave a shot, it might rapidly drop).
I know we were lucky to have a year with our cat after his first hypo. But he had so many miserable trips to the vets, so many subsequent hypos, and I had to jab his poor ear for a blood sample at least twice a day -- and after all that we still couldn't save him. Now I think that after a certain point, some diabetic cats will become unstable and there's little you can do about it. Our cat basically had 24/7 supervision, and we still lurched from crisis to crisis.
And please don't feel bad about your cat spending the night alone. My cat never had seizures (I did have to rub honey on his gums several times, and rush him to the vet), but the earlier stages of low blood sugar were always disorientation, then grogginess, then just sitting in his basket with a glazed, unresponsive look, like someone who'd had too much wine at lunch. He was very out of it, but didn't seem in any pain or even discomfort.
Sometimes I only caught an incipient hypo from doing a random late test; it was hard to distinguish from standard sleepy cat lazing around. So even if humans are to hand, it's easy to miss, especially at night (as insulin may not peak until you're in bed). And, from what I've seen, the cat has less and less awareness of what's happening as blood sugar drops.
Apologies for this long post. Of course you feel so sad to lose your cat; I'm miserable without mine, too, a happy sociable flump who'd been with us through so many house moves and life changes. But please don't feel additionally bad about the circumstances, because it sounds like he had great care from you and your neighbour, and this was a case of a well-managed chronic condition taking a sudden turn.