In Origins, I think Alistair mentions old Templars are put out to pasture when they become too Lyrium-addled to function properly, usually enjoying their remaining years being cared for in a monastery. The Chantry does take care of them, but it's still pretty bleak fate when you consider it.
I wanted to touch on this particular subject, since I work in an adult assisted living home for the elderly. I can picture these poor Templars, older and their minds addled from lyrium, much like the people that I have to care for who have dementia or Alzheimers.
I never realized this before. I might have happened across it in the game, but forgot about it over the years. Anyway...
Imagine as an Inquisitor, for some reason, you have to go to one of these monasteries where Templars are "put out to pasture", and you have Cullen with you. Some of these older people are sitting quietly at tables, others are speaking softly to themselves, stuck in a loop from a time long ago, and they think they're speaking to someone who isn't there. And one is suddenly set off into a screaming rage, because something they see suddenly reminds them of a horrible incident with a mage, and the nuns have to rush to restrain him and calm him down, so he won't hurt himself, or anyone else that is there. These nuns have to dole out small portions of Lyrium, feeding the old templar's addiction, because to take them off of it entirely would be too cruel. Some of these old templars are so far along that they can't feed themselves, they have to be fed by the nuns; and they can't tell when they have to go, so they have to wear cloth diapers like a baby. The nuns have to change them when one soils himself.
What a bleak future indeed. I hope there's some way to get Cullen off the stuff before it's too late.