The first question is always where the damage is. Punctures in the center tread area, from a nail or screw, are usually repairable. Damage in the shoulder or sidewall generally isn't, because those areas flex constantly and a repair won't hold safely.
The second question is size. Small punctures from nails and screws are typically repairable. Larger cuts, gashes, or tears aren't, no matter where they are.
The third question is how far the tire was driven while flat. Even a short distance on a flat tire can crush and damage the inside of the sidewall. From the outside it can look fine, which is why we inspect the tire before deciding anything.
If the tire passes all three, we repair it and you save the cost of a replacement. If it doesn't, we'll show you exactly why and quote a replacement, new or used. You'll never get a replacement pushed on you when a safe repair would do.