It depends...
why are you writing unit tests?
1) to check the code you are about to write
2) to check the code that you already wrote down
3) to check the code that someone can write in the future
If you are writing code to verify something that you are going to write, write it for the requirements of the code you are going to write.
If you write tests to test your code, check the code you write.
If your written tests do not allow other people to modify your code, it is not your responsibility.
Example
You have a base class A with a specific method, M. You have tested this method back, side and upside down. Then you create 3 subclasses of A and name them B, C and D. You add new functional methods for classes B and C.
You should check the new methods of class B and C because this code has not been verified, but the method M from class A has already been verified.
You redefine method M in class D, add code, and then call the base method M. The new override method should be tested and should be treated as a completely new method. unit test cannot confirm that the base class method M has been called.
Writing the same test 4 times does not help anyone. Every developer should rewrite tests for the code they write. If this code is tested, and the tests meet the requirements, and the tests pass, then the code is good.
Carrying out the same exam three times in a row is pointless.
On the other hand
We do not live in an ideal world, and if you have problems with other developers who do not test their own code, it may be useful for you to do the work for them. But understand, itβs not your job to check the code that they write is what their work is.