A solicitor can't drop one of their clients out of nowhere. Once they have agreed to take on a case, they agree to follow it until the end.
If a solicitor wants to end their representation of a client, they are required to send a written notice explaining the reason for termination, what actions the client can take to avoid termination, and the deadline for taking those actions.
If the solicitor fails to do so and terminates the client's representation regardless, they would be in breach of contract and may not be entitled to receive payment.