It's nice to see you here in the Community, corneliakow.
Let me help you go over to your QuickBooks and get this client inactivated. You can review your client's transactions so you can identify why he/she a non-zero balance.
Here's how:
Click Sales in the left panel and select Customers.
Find and click the client's name to open their profile.
Hit Transaction List.
From there, you have the option to delete your customer’s transactions. This way, your client now has a non-zero balance so you can mark it inactive.
You can go through these articles to help you manage your clients as well as your QuickBooks account: