Interesting thread this - and there are probably as many answers as there are chefs. The first place I worked in pre-cooked the chicken / lamb and then reduced the cooking liquor to a stodge that they then tipped into the cooked meat. If you ever scraped a pan with a spoon, this was heaven. I tried it myself but kept catching the stodge on the pan, so now we just keep the protein in the cooking liquid and spoon a chef's spoon of the liquor into each portion. The enhancement to the flavour of the sauce is considerable - so much so that we now add veg stock to some vegetarian dishes to build up the umami in the same way.
Which brings me to not one but several occasions on which I have asked chefs what they do with the pre-cook liquor, to be told that it goes into the gravy. I once asked if this might be an issue for the dishes on the menu with a green "V" against them, and he replied "Makes vegetarian taste better." Hmmmm.....
I have heard stories of it being poured down the sink but can't say I have seen this. If true it's a terrible waste.