"caved in on" is correct and usable in written English.
It is typically used as an idiom, meaning to collapse or to give in, especially under pressure. For example: After hours of negotiation, she finally caved in on the proposed contract terms.
"The world caved in on us," she said in the recent interview.
"It is fairly clear that the government has caved in on this one to big business because there is nobody else arguing that plain or standard packaging should not have come in," he said.
A 30-foot-wide, 10-foot-deep crater of dirt and asphalt yawned on 79th Street between Fourth and Fifth Avenues after the street suddenly caved in on Wednesday afternoon, nearly taking one resident's car with it and drawing a crowd of onlookers.
Relatives hugged, kissed and thanked God as news of the message reverberated outside the entrance to the mine, where they had been camped out since the mine caved in on Aug. 5. "We never, never lost faith," said one family member, Eduardo Hurtado, as other miners' relatives waved red, white and blue Chilean flags and cheered.
As soon as the roof closed, however, it caved in on Murray.
Then came the videotaped sermons and the roof caved in on Rev. Wright's reputation.
Obama then caves in on pretty much everything in return for letting it look as though he is running the country.
Caving in on fuel is only one about-turn.
The first time I saw Lamby, I winced -- my chest felt like it was caving in on me like it does during one of my anxiety attacks.
At the moment, an agreement seems to be hinging on the players caving in on the final points of contention.
It's not as if McCain has been caving in on anything important, like economic recovery... (Feb.
