as far as i know, all the cars, esp taxi have insurance - Third Party, Comprehensive plan, and theft and fire etc...

the 第三者责任险 should be compulsory (as far as I can remember) , and it includes the third party （include passenger）索偿 , so if anything happens to the passenger of the taxi, the passenger can ask the taxi driver to 赔偿 and the taxi driver can ask the insurance agent to 理赔

of course, with all kinds of receipt, it is easier to settle the 索偿额。and most of the time, insurance 理赔 happens after the 乘客 is discharged from hospital becasue at that time, all exact figures come out.

Not sure if the above answers your question, hopefully it can give you some basic idea:)