The one framework I can see as feasible for euthanasia is where active treatment has been considered not to be in a person's best interest and they are dying. Or somebody with capacity is refusing active treatment and as a result is dying.
Eg: end stage dementia (or cancer or insert other terminal illness reaching it's final stages and capacity has been lost) and a decision has been made NOT to insert a feeding tube or otherwise to force feed, or administer treatments such as IV fluids or antibiotics. The person has no interest or ability to swallow food. Their life as it remains is characterised by either sedation/catatonia or agitation. They are being managed on a comfort pathway being treated for pain, agitation and so forth, waiting for natural death to occur, as it inevitably will. All of the above is already possible and is not euthanasia.
Or eg somebody with capacity who is reliant on intensive medical intervention to remain alive has made a decision, with no other means available to end their life (owing to their illness or disability), to refuse all medical intervention and in doing so intentionally die naturally (often by starvation).
Natural death in either of these kinds of circumstances may be protracted and involve suffering. In that context I can see it being possible to legislate for euthanasia, essentially to hasten natural, inevitable death, without there being a much of a slippery slope. Existing ethical standards on withdrawal of medical intervention (either in line with best interests or because of capacitous refusal) would cover the same criteria.
This would be offering a 2nd way to die as it were. Options: 1) Accept active intervention which may prolong your life but be uncomfortable / cause suffering, 2a) Decline active intervention and die naturally or 2b) Decline active intervention and die sooner / quicker / more painlessly with a bit of help. And you can't have 2b) if 2a) isn't a possibility. Eg those theoretically capable of remaining alive without medical intervention don't get access to euthanasia.
Severely disabled people who lack capacity but are currently kept alive because it is considered to be in their best interest to receive supportive and medical treatment, are unaffected as their best interests haven't changed. As 2a) already isn't on the table, neither is 2b).
This would be about hastening death in the actively dying, at the point at which medical intervention to prolong life is being abandoned in any case. I don't think it would save money at all, it would probably cost more money but I do think it would reduce suffering at the end of life.
Edit: the thing is, as I said previously, I think the biggest hurdle for most people suffering a prolonged death, that needs no new legislation whatsoever, is accepting / deciding that the time to stop aggressive medical treatment has come. Eg being able to recognise that hauling somebody bedridden with dementia into hospital for IV fluids, antibiotics and subjecting them to the pain and indignity not only of treatment but of the inevitable delirium/agitation that will accompany it, is just cruel and pointless, and goes against their best interests. So for the vast majority of people what is needed is not a discussion around euthanasia, but a discussion around advanced care planning / advanced directives, best interests and the futility of many medical treatments in terminal illness.