I'm planning to submit papers from my completed PhD thesis (finished less than a year ago) but recently found that unfortunately, my supervisor who had a significant contribution to my thesis is not well and not available for a review, preparing for chemotherapy :( What would be the ethical way of publishing papers and respecting their intellectual contribution without inconvenient communications with them at this stage? Thanks, in advance, for sharing your suggestions
My suggestion is that you submit in the normal way, but several days (say a week) beforehand, send her/him a note that you are submitting, along with a copy of the paper. You seem to indicate that the supervisor should be a co-author (field dependent)and if so, do that also.
In your note say that submission is pending unless you are advised against it. Make the note itself short so that little effort needs to be spent to make a quick decision. In particular, don't ask for a review and revision of the paper.
"I expect to submit the enclosed next week unless you advise differently... I will wait if you prefer.".
If you don't get a request to wait then just submit it. If they are well enough to review it, they probably will.
Of course, if there are no time constraints/limitations, you can also just wait.
But note that if the situation is dire and your advisor is near death then it is time for you to step in to the legacy along with his/her other students. You will have sole responsibility for these situations soon enough in that case.
My suggestion would simply be to respectfully ask your advisor, or your advisor's family, what they would prefer. They may give you a go-ahead to handle everything, or not mind having something familiar to review to take the mind off the impending treatment. Overall though, be prepared to be patient.
Randy Pausch's "Last Lecture: Achieving Your Childhood Dreams" (https://www.youtube.com/watch?v=ji5_MqicxSo) shows that cancer needn't make one unavailable. I cannot speak for your PhD supervisor, but you should consider the possibility that they are continuing to work. (The precise situation is unclear from your question.) If they are, then you should communicate as per usual. (Whether you mention cancer depends on the relationship you have with your supervisor.) Otherwise, Buffy has some good advice.
The OP comments:
you're right I cannot decide for my supervisor to continue working on the studies or not but the question is how can I get the answer without inconveniently communicating with them about this unrelated issue at this challenging stage of their life
Your supervisor may not consider communication inconvenient; they may expect you to proceed as usual. Perhaps you can establish your supervisor's preference without communicating directly. (E.g., by contacting someone from their department.)
If you do follow Buffy's advice, then "several days (say a week) before[ submission]" is not enough, since your supervisor may be busy during that period (e.g., receiving and recovering from treatment, on holiday, working, ...). Give them at least twice that, maybe even a month.