I would assume that a club is expected to have done a medical assessment of a player prior to signing a new contract to protect their interests. During that assessment they should identify pre-existing conditions that might or might not present a future risk during the term of the contract.
So if a pre-existing injury gets aggravated to the point where it impacts on a player's ability to perform and it can be identified as such, that risk I expect falls back on the club.
But if the player happened to get a new injury whilst playing, for example a serious neck injury, and the player is advised by a doctor to cease playing immediately, then I would think that is where the insurance steps in to compensate because this event was unexpected and therefore unforeseen by his club.