An orthodox married lady hit my car and requested that I get an estimate and charge her out of pocket and please not go through her insurance.
A few days later I chanced upon the Mishnah in Perek Hachovel which says that one cannot charge a married woman for damages she causes as she currently has none of her own money.
Her husband cannot be held responsible as he did not cause the damage.
All that can be done is get an estimate and charge her if she would ever be single again, chas v’shalom.
There are nichsay milug options as well but all this is novel to me and I have never heard of any sort of custom in this topic.
Although there is such a concept, in your situation she does have to pay. The husband doesn’t have to be held responsible, she has insurance, which can pay it. Additionally, many women nowadays do have their own money, from before their marriage, or if she has a good job.