According to: www.theidioms.com, the phrase "pigs might fly" or "pigs may fly" has been used in various forms since the 1600s, when it was said that "pigs fly with their tails forward", used as a sarcastic remark something overly optimistic. The form "when pigs fly" is more common in America.
It is a phrase that when hears all the time under a myriad of circumstances. When I was in medical school (I graduated in 1966) if someone said that someone with a dangerously slow heart-beat (bradycardia) would one day be "cured" by a gizmo smaller than a hockey puck and nowadays a quarter, or that heart failure due to a narrowing of the mitral valve secondary to rheumatic heart disease could be cured by surgery in which two fingers inserted into the heart could "split" the mitral valve and cure the cause of the heart failure—yes and if pigs could fly. I experienced these two miracles of modern medicine in the early part of my career and have participated in recommending scores of patients, especially older ones from the likelihood of certain death to be able to live ordinary and full lives.
As for end-stage organ failure—I experienced in my early career the miracles of kidney transplants. As an intern at Boston University Hospital in 1968 I admitted one of a set of twin early adults, apparently identical twins. One of the twins had renal failure and the second healthy kidneys. It was the early days of renal transplants with only live donors (usually family members) with the only alternative treatment being dialysis for the remainder of one's life. Home dialysis was just being developed with the finding that peritoneal dialysis could be as effective of hemodialysis without the burden of expensive machinery and the burden of attending a dialysis centre for a day's treatment. According to various on-line sources, "the history of dialysis dates back to the 1940s. The first type of dialyzer, then called the artificial kidney, was built in 1943 by Dutch physician Willem Kolff: Holff had first gotten the idea of developing a machine to clean the blood after watching a patient suffer from kidney failure."
Over the next decades the apparatus became smaller and more efficient as new technologies were developed—but no matter how good the machine it required a number of treatments a week at a dialysis centre to be successful. According to historical courses attempts at peritoneal dialysis go back over a century but were plagues with complications such as infection. According to a 2010 article in Dialysis & Transplantation, Volume 39, Issue 8 p. 338-343 "In the late 1940s, Fine and colleagues reported successful peritoneal irrigation in a patient with severe anuria, who survived after four days of continuous peritoneal lavage. This was indeed a landmark in the history of treatment of uremia using the peritoneal cavity. In the late 1960s, intermittent peritoneal dialysis (PD; provided once or twice a week in hospital) was practiced worldwide. In the late 1950s and early 1960s, intermittent PD became a safe and standardized procedure. Further advances were primarily related to catheter improvements that made long-term therapy possible."
A transplant between apparently identical twins as we were faced with in Boston seemed a good prospect. My patient was the donor who was on a medical ward while his recipient brother as on the surgical floor. The surgery went well but during the night (I was on call with another intern from surgery) my patient started bleeding from the site of his surgery. I called the surgeon who said we should cross-match two units of whole blood and see what happens. I was loathing to administer donated blood (the hospital did not have a substantial blood bank) as in the building in which I lived was a private blood donation facility. I would see the donors waiting in line when I went to work and some were there sooner, from my recollection, that the requisite three-month wait. Also many of them seemed to be giving the blood because of the $25 fee they received for the service. It was about this time that what was called Australia Antigen was identified which seemed to be the cause of a type of hepatitis. It was later reclassified as Hepatitis B and indeed was the culprit in a more serious type of hepatitis that was caused by the more common and less serious Hepatitis A.