In principle but not magnitude, especially if you've relocated.
Usually you cancel any other pending offers once you've accepted a position if you're nice, and that could close some doors because someone else takes those jobs. Might even get you red-flagged if you go back to them and say "this company lied to me so I quit" (the other person has no way to verify that's true or you blew up on someone verbally the first week and got canned).
Someone correct me if HR can give the termination reason, I don't remember.
Asking a prospective employer what your references said about you if they pass on you sounds like a tall order. I'm lucky if I can even get a response to a cover letter + resume, definitely have never been given feedback about a sample project solution or interview (other than hired or not).
Am I wrong and it's actually one of the easier pieces of feedback to get?
[1] http://www.legislation.gov.uk/ukpga/2006/35/pdfs/ukpga_20060...
[2] https://cdn.prospects.ac.uk/2.0.9/pdf/Graduate-Employment-Fr...
https://www.dailymail.co.uk/news/article-1260901/Woman-lied-...
Normally they probably get around with:
And any other duties, bla, bla, bla
So it's hard to see a shift in the onesidedness of the relationship
What about what they say on the interview? Verbal contracts are valid in some circumstances ... Record the interview ... :)
Someone more left/anti-capitalist might argue that this is disproportionately in favor of the employer. The employee is depending on this job for food/shelter. Replacing the employee is much less disruptive to the employer than the employee. Especially considering the employee may have had to move to the area for that job.
http://www.shakelaw.com/blog/lying-on-your-resume/
Mostly it's just the risk that you'll be found out and fired (which is similar to the risk on the other side of the table— that the employee will find out and quit).