I boiled some chicken last week, and saved the stock for future use. But, as I don't have enough freezer space, I just put it in the fridge, so it has been liquid.
Since, it has been a week, is it still safe to use?
Chicken broth is one of the most perishable foods there is—it is nearly a perfect growth medium.
The FDA recommends storing it no more than 3-4 days.
I would recommend only keeping chicken stock two or three days after cooking - much like cooked chicken itself.
If your stock was made with vegetables, I would keep it for even less time - not because of safety, but because vegetable stocks quickly turn bitter.