Theoretically, such a possibility is not excluded, but it is not applied in practice. In this case, an accident could damage internal organs, which is why they cannot be transplanted to another person.
Good question. It is worth considering a huge number of factors, but, in my opinion, the most important of them is time.
For example, a child received a kidney transplant as a child. Then he led a healthy lifestyle and lived in this way, say, up to 40 years. At the age of 40, due to an accident, he gets into an accident, as a result of which fate does not give him a chance to survive, and he, having become an organ donor in advance, donates his kidney to some seriously ill person. In this case, the re-transplanted kidney, if successful, will function as any other kidney in a healthy person should function.
Or here's another example. A week ago, a person who received a kidney transplant had an accident while being transported from one medical center to another due to unforeseen circumstances. Naturally, the body is not able to provide the viability of a recently transplanted organ, so it is unlikely that this kidney will be transplanted a second time.
If the answer is not correct, I will gladly accept any criticism.