To foist off is to pass something unwanted or inferior to someone else through deception or pressure: He foisted off his old car on his nephew, They tried to foist off counterfeit bills at the register.
The phrase emphasizes getting rid of something by making it someone else's problem.
Plain foist carries the same meaning: foist responsibilities onto others.
1. imposition — impose, Force acceptance of; burden (Oppressive weight or duty); dump on (Attack with complaints); inflict (Cause to be suffered); obtrude · intrude · unwanted · unwelcome · encroach · presume · pushy · offload · pass along
2. deception — unload, Remove contents from; swindle (Deception for financial gain); con (Argument against); scam (Dishonest money-making scheme); fraud · misrepresent · counterfeit · fake · sham · dupe · deceive · trick · hoodwink · bamboozle