The rider (at that level) is employed by the team, the team are required by the UCI to have at least travel and 3rd Party insurance although whether any of them require the rider to have personal insurance is a different matter. the rider will also be covered by his home Federation and most riders at that level will have full personal accident/life insurance cover, either through the Home Federation or through another insurance policy.
And there’s the unwritten rule that, in the thankfully very rare cases when a rider dies during a pro race, the following days prize fund (which can amount to thousands of euros) gets donated to the next of kin.