A client asks for an 8-character vanity address, knowing the cost is too high.  After one (or more) 7-character partial matches have been found, the client cancels their request.  Now what?

Maybe the client wanted a 7-character address in the first place.  Depending what information is public, the client may have their 7-character address for free, and neither you nor the miners get anything.

Maybe the client wanted a 7-character address in the first place.  Even if partial matches are secret, a miner who found a 7-character partial match may negotiate with the original client for the 7-character match.  Neither you nor the other miners get anything.

I would suggest that a refund should deduct *something* related to the value of work done so far.  The deduction to be paid to the miners for work already performed.