the short answer
Fire a coaching client when the relationship costs more than it returns and one honest reset has not changed it: chronic non-compliance, boundary or respect issues, work outside your scope, a values mismatch, or repeated payment problems. Do it in one direct, kind conversation, confirm the end date and billing in writing, settle payment per your contract, then remove access and hand over what is theirs. Done well, a former client leaves as a respectful ex-client and a quiet referral source, not a bad review.
This is general information for coaches, not legal advice. Refund and notice rules vary by country and state, so follow your own contract terms and local consumer law - and remember that ending with a client who needs care beyond your scope is a referral, not a failure.