Been there myself and seen it in other places too.
It can actually be a good filter, prospect-wise: a company that does gossip about/blame an ex-employee for some of their failures is advertising their own lack of agency.
If they were smart, they wouldn't gossip, and not even let the gossip go. That's very bad strategy, both internally and externally.
If they're not, well, I can't tell you what to do.
What happened to me:
1. first I spent several horrible months expecting my whole career to be over;
2. until I realized my ex-employer and its own reputation in the field was totally irrelevant and could not harm much my reputation (or better yet, act as a useful filter);
3. when looking for employment, when relevant, I explicitly mentioned this experience and what came with it, and what I was then looking for in a new company/position/team, so that I was the first to pitch what did happen and how I reacted to it.
It served me well.
Those that listened to my story and took the time to understand it turned out to be great teams to work with.
Those that dismissed me on the spot, well... I can't say really - but what I heard of afterwise from ex-employees was kind of reminiscent. :)