I'm a volunteer EMT with the ambulance service in my town, with several 'assisted living' facilities in our district. My rough guess would be that 25-30% of the folks we take to the hospital are in the last year of their life, and likely will spend the rest of their days in the facility where we picked them up (with occasional 'field trips' to the ER).
While it's popular to complain about these sorts of calls (they certainly lack the excitement of a car wreck, or the glamour of saving a child), I generally enjoy them. Even in the grips of dementia, many of these people have fascinating stories to tell. We're stuck together in the back of the truck for 20 minutes... I can either get a head start on my paperwork, or I can engage them in conversation. In the past month, I've met a WW2 bomber pilot (who flew in a pathfinder squadron) and a former Rockette (plus a schoolteacher, a librarian, a surveyor, and several others I'm sure I've forgotten). I learned something from each of them (well... most of them... grumpy old people are still grumpy...).
The statement "I just try to treat my passengers the way I would want my mother treated," really rang home for me. I've heard that same sentiment (practically verbatim, just s/passengers/patients/) from several providers, all of whom I regard very highly. I think it's one of the best predictors of someone's ability as an EMS provider. While I know a few extremely capable medics who have a lousy bedside manner, every medic I know who seems to genuinely care about their patients is a top-notch medical provider.