Let's say for argument's sake that if I buy a rotisserie (cooked) chicken from my local grocery store and stick it in the fridge it will last 5 days before it starts to be detectably going bad. Prior to the 5th day the bird tastes and smells fresh.
If I rip the meat off the bones on the 4th day and fry it in some olive oil and/or butter and stick it back in the fridge should I expect it to stay good another 5 days?
100% with moscafj on what constitutes good/bad and if no detectable bad means OK. The key point to your question, does doing anything to aging food, be it add ingredients, re-cook or reheat it, etc. reset the clock, effectively: NO. If food has aged, it is aged, and there is little to nothing you are going to do to effectively reset that clock.
OK, that statement is not absolute, many raw foods will spoil faster than cooked, and some foods you might be able to slightly extend. I am thinking things like your chicken example. Wait four days and then try to extend its useful life another 5, no, not going to happen in my opinion. But, lets say it is 2 days old, and then you make a soup. Maybe you will get another 4 days from that before it starts to get iffy, but not much more than that.
Never are you going to undo any of the aging, regardless of if it is going bad or just becoming lower quality, but for a time you may be able to find an application that is still is good enough quality if safety levels have not been passed. But, it it actually has started to go bad, you may kill some of the active bacteria and the cost of very overcooked product, but few toxins will be removed and some of the active pathogens take more active killing that heating to a still palatable level will accomplish. There may even be a few instances this is not true, but I cannot imagine meat being one of them. (Personal bias, but I always also assume that grocery store prepared foods were likely items that were close to shelf useful life limits to begin with, so I assume a shorter left-over life than if I had bought the item fresh and made it myself.)
There are several things to consider here. Fist "detectably going bad" is probably beyond the point where there are potential safety issues. Second, it is probably difficult for you to determine how long the chicken may have been in the danger zone between grocery store cooking, storage, travel time to your home, and refrigeration. Consider how long it might take a whole roti-chicken to pass through the danger zone and cool to safe temps. So, you have a potential opportunity for bacterial growth to begin with. Thirdly, smell and taste are not reliable indicators of safety. Plenty of potentially bad stuff happens with out you sensing it. Fourth, what you cook it in (oil or butter, for example) is not relevant. Finally, reheating generally does not reset the safety of your food, especially with the unknowns that you presented in your query. For example, food heated poorly, multiple times, could support bacterial growth that becomes more heat resistant.
