You have to do something really, really, really out of line in order to get kicked out of residency training. Program directors face substantially high-powered incentives to avoid things like this happening, because booted residents (a) create all sorts of problems with regards to service coverage, (b) depress morale among remaining residents, and (c) undermine your ability to attract a strong class the following year due to the general paranoia and conservatism that characterize graduating MS4's.
One of my close friends trained at a highly competitive ob/gyn residency program in New York, and last year they graduated an assassin. (I don't use that term lightly. There were serious concerns not just among attendings but among her fellow residents about patient safety.) There were signals as early as this resident's PGY2 year that she was becoming an assassin, but each class of chiefs just kicked the can on down the road. When she graduated, the program director (who normally helps each resident secure jobs, fellowships, etc) didn't really lift a finger for her -- but that was the extent of any corrective action (and it wasn't really corrective, just punitive). There was never any serious talk of holding her back for remediation or not graduating her. This year there is a budding assassin in the PGY2 class of the same program. They are making half-hearted attempts to remediate her, but in general the entire program is tiptoeing around the issue because the new assassin, like the graduated assassin, is African American and nobody wants to come out and say that the only 2 weak links in the chain in the program's recent 5-year history were the only 2 African Americans.
All of this is to say that, in general, with the obvious program-to-program variation, if a resident gets kicked out, something went really wrong and it probably didn't happen for no reason at all.