Sometimes a contract will specifically say that one party may end the contract if there is a particular kind of breach (or perhaps any breach) by the other. Any clear provision to this effect will be decisive.

If there is no express provision, the general rule is that a very serious breach by one party will allow the other party to choose whether or not to end the contract.

To be serious, the breach would have to be either:

If the other party's breach is very serious, the person affected can choose to go on with the contract (and still potentially keep their right to claim damages), or end the contract. If the contract is terminated, the other party should be advised immediately.