The phrase "under pain of" is correct and usable in written English.
It is typically used to indicate consequences for failing to abide by a condition or rule. For example, you could say "all students must complete the assignment by tomorrow, under pain of receiving a failing grade."
Sample "pay sheets" were attached to these reports, signed by selected prisoners under pain of death.
Happy by Pharrell Williams would be banned, under pain of exile or worse.
What of the mentally ill and the homeless banned from begging under pain of criminal sanction?
You are forced, under pain of death, to quit all that silly ideation and pay attention.
She says he said that bishops shouldn't notify the police about allegations of child abuse under pain of excommunication.
So O2 probably has it, although no-one will confirm under pain of death from Monsieur Jobs, I imagine.
Aamer's supporters claim he suffered terrible abuse at Bagram air base and that an alleged confession he made to captors was obtained under the pain of torture.
It stars an Oscar winner in a role so comprehensively wrongheaded that logic dictates he must have been blackmailed into it under actual pain of death.
And so one finds oneself here, in the strange position of looking back somewhat indulgently on the "lesser" offensiveness of George W Bush, under the pain of whose presidency, threatening to leave the US was considered a rather jolly and vainglorious overreaction.
Until now, he has had little to show for it: even under the pain of punishing economic sanctions, the Iranian government has shown little interest in negotiating a deal with Washington on its nuclear program.
His 20-stone outline is crouched awkwardly under the pain of embedded lead.
