CBSubs is not designed to allow for retries for disputes; it can only handle them for failed recurring payments. It is recommended to not configure Stripe to retry. Currently no it will not send a cancellation if a dispute is lost. Within Settings > Automatic collection under "Manage failed payments" it should be configured not to retry. Have added a feature ticket to review sending a cancellation to Stripe if dispute lost.

forge.joomlapolis.com/issues/7578

That is not a visible option. Only choice is to choose the calendar to retry.

You have to select "Use custom retry schedule" under "Manage failed payments" then set "Subscription status" to "cancel the subscription" for it to not retry payments. The reason retries won't work for CBSubs is on failed payment webhook we cancel the basket out. If Stripe doesn't do the same you end up in a situation where a payment could be billed twice. I'll be reviewing in a later release to see if we can better support Stripe retry attempts somehow assuming the failed charge webhook has information stating it's going to retry otherwise we just won't have any reliable information to go on.

One setting in case of failed dispute say "set the subscription as unpaid" instead of "cancel the subscription"

Wouldn't it be better to choose "cancel the subscription" in this case ?

Yes, that should be set to cancel the subscription to allow Stripe to clean up after it self. Otherwise in a later release we'll force the clean up with a cancellation API call.

Stripe should be doing that it self. It doesn't make any sense for Stripe to keep the subscription active for a lost dispute. CBSubs Stripe cancelling the subscription at Stripe when a lost dispute IPN is sent has not been implemented; you can track this in the below feature ticket that was provided above.

forge.joomlapolis.com/issues/7578