Refers specifically to eviction from rented residential property for failing to pay rent.
Occasionally, landlords will warn their tenants who are behind on rent with this euphemistic term.
During the recession, lots of people cannot afford their rent, so they are being "pinched."
He is behind on his rent; therefore, he is facing "pinching."
According to some interpretations, the song "Pinch Me" by the "Barenaked Ladies" uses this term with this meaning. The narrarator is unemployed and cannot pay his rent, and he is resigning himself to his inevitable fate of homelessness.