This happened to me as well. Interviewed, was hired, received deposit, went to two prenatal meetings, then I received a call of "Hey guess what? We had the baby yesterday." Mom said she went for a prenatal OB visit, baby's heart rate was high, they sent her to hospital, then did a c-section, and there was "no time at all" to call you.
Except the more mom talked, the stranger her story got; she went home in between OB visit and hospital to pack some things, call family, etc. Then had to wait about 4 hours at hospital until OB arrived, re-checked baby, etc. and decided upon surgery.
I could tell by the tone of the phone call that it was assumed she wouldn't pay me anything else since I wasn't at the birth. I offered to come for breastfeeding support, then a postpartum, etc. All were refused and I finally brought up the subject of payment.
I explained that I only work with 2-3 clients/month, can not influence specific outcomes (i.e., precipitous birth or un-planned c-section) but that I potentially turn down other clients to work with this mom. In the end she agreed with that reasoning and sent me a check, but the whole situation felt weird. Always had from the beginning (really felt like mom was hiring a doula because it felt "in vogue" to do so (?!?!) rather than because they actually wanted to the support.
Lesson learned? Trust my gut about clients from the get-go, and make sure my contract is exceedingly clear!