Is there a way to determine if the user closes the tab he is doing?

There isn't any way to do that but there must be a workaround for your use case using timer exceptions. Can you explain your use case more?

I wanna only user open record from record list. It mean, if a user has already opened the claim, then it should come locked for second person .

My question is my way to resolve this problem, I thinks so that

You can use the textCache plugin to set a value in some key. For eg. lets take the key as ClaimSummaryDb and set the user context of loggedInUser() in this. 
Now everytime when you load that screen, get the value of that key and check if it is null. If not, then show a lock else allow to edit. 

I do recommend doing this. The record itself is meant to only display data. Related actions are for taking action. If you need to prevent users from starting two related actions for the same record, I suggest implementing some locking there.

yes, what is your solution for that ?

Do you have document about textCache?

https://community.appian.com/b/appmarket/posts/text-cache

Once you download the package, you will find a README file that can guide you. 

Thanks so much.

https://community.appian.com/w/the-appian-playbook/196/data-locking-strategies

thank you.