"At what expense?" is a valid question and so it is a valid sentence.
At the expense of enternaining or damaging
Ashley decided not to buy the purse because she couldn't afford the expense.
I stayed up all night to finish my essay, at the expense of my rested brain.
I kept an expense accounting to give to my boss. The expense of the planned trip made me change my mind and stay home.
My expence is very high.
No expense was spared on my daughters lavish wedding.
In our contemporary society, prices are becoming very high as is the expense of gas.
As a verb e.g. " It was necessary to recalculate the expense budget " .
Additionally we wanted add an extra room but the expense was to much.
They can treat this condition at their outpatient clinic so I can save the expense of a hospital stay.
Once Beth purchased the stamps for the committee, she sent her receipt to the treasurer to reimburse Beth's expense.
The school board found that replacing broken windows from vandalism is a major expense.