I am a PhD student in Economics at one of the top five universities in India. I am on the job market now, applying for postdocs pretty much anywhere in the world (as long as there are people with overlapping research interests).
Situation: After a few years of lowkey power abuse, it all recently escalated to textbook workplace harassment, and my advisor (the abuser) has now decided to withdraw all his support from my future job applications, notwithstanding the following facts: (a) out of my eight papers, six are 100% my work, the other two he made at most 5% contribution, and yet he has imposed himself as a co-author in all of those (five of them are already published/in the arxiv), (b) he has also made me do his referee work in the past.
In effect, he won't be writing me any recommendation letter. Not only that, he went out of his way and falsified information about me to some higher authorities in my university (not that that harmed me in a major way, because some faculty here know me better). So after all this, I probably can't even ask for letters from him in the future should he happen to change his mind; I am almost sure he would write downright lies about me.
Problem: Despite having a very good track record of publications, I am facing the possibility of being forced to leave academia for no fault of mine (well, except naivety).
Sidenote: Some of the higher authorities in my institute know about this, and so do my other letter writers; and they expressed sympathy and support towards my cause. However, at this stage of my PhD (my thesis has already been submitted) the faculty members who know the details of my case and support me are powerless to help me in any practical way. We don't have a clear-cut HR either.
So, my question is this: if the postdoc selection committee (and, in the future, for tenure-track positions etc) comes across an applicant, who doesn't have his PhD advisor's letter (an advisor who happens to also be the co-author of at least five papers), but all the other letters are mostly positive, what are his odds?
P.S: I know this doesn't speak well for me; after all, how did I let something like this happen? How did I not see the red flags and switch advisors when I still could? I won't get into the details and defend myself, but I'll just say that mistakes happen, and this time I made the mistake of not switching advisors when I still had time and now I'm beating myself up over it.
P.P.S: I haven't gotten into details of abuse but if it comes up in the comments, if anyone asks, I will edit and add some examples.