"To absorb the cost" means to bear or take on the expense or financial burden of something without passing it on to others, such as customers or clients. Full definition
Every year thousands of animals are euthanized or sent home to die because the people who love them can not financially absorb the cost of veterinary care. (okcpetsmagazine.com)
The remaining bond fund holders will be forced to absorb the costs associated with the bond valuation discounts being applied. (investopedia.com)
The logical, which is to say the fair, way to address this situation would be to make the driver absorb the cost for his slice of the damage. (carbontax.org)