Say I were to be cooking chicken in a pan, and I'm using tongs to flip the chicken periodically. By the time the chicken is done, how can it still be safe to use the tongs I started with to handle the chicken? Obviously it's come into contact with raw chicken, so why would I want to handle my food with it. Should I be switching utensils or washing them mid cook?
There are several aspects to this:
My rule is to minimize reuse of utensils, but I don't have 10 pairs of tongs and someone to wash them for me, so for some meals it happens, and as long as it's not chicken, I don't worry about it.
The simple answer is that they don't remain safe: this is a risk factor for cross contamination.
It is not appropriate to use, for example, the same tongs to put raw chicken on the grill as to flip that chicken later.
In practice, the risk may be low, because even if the utensil is contaminated, the main food is at temperature and renders it safe within seconds. Also, the volume of food on the utensils is small, and the length of time is short, so there is not a huge risk.
Still, it is best to remove fully cooked food which will not stay at safe temperatures with fresh, clean utensils.