When writing a paper, it's not that seldom, that I want to cite papers where a DOI is given but cannot be accessed (anymore). Quite frequently, the corresponding DOI is also presented within the PDF document of the paper that I want to cite, which is also not accessible (anymore).
The intention of DOIs was to guarantee permanent access to documents and unify it, but in reality, some are broken over time. Furthermore, not every DOI lookup website does have a complete list of all DOIs.
My primary question is: Is there some common practice how to handle this situation? Should I provide the DOI as well in my references, even though it is not accessible anymore? (Maybe it could still be accessible with some other DOI lookup website?)
What is the best DOI lookup tool? Is there something better than https://doi.org?