The answer to this question depends on which version of MemberMouse you are running.
If you are on versions 3.0 or above: The MemberMouse plugin will remain active if your MemberMouse account is canceled. Onsite billing through Stripe, SmartTags™, checkout, access control, and front-end functionality will continue.
You won't be able to manage any of the Stripe subscriptions through MemberMouse, though. Once you've canceled, some settings and backend options will become locked, and they cannot be changed until the license is reactivated.
If you are on versions 2.4.6 or below: The plugin will deactivate after the license check pings your site. This deactivation may be immediate or within a few days. If you integrate with Stripe, MemberMouse handles recurring billing, so if you deactivate the plugin, recurring billing through Stripe will no longer happen. All functionality, including the login, emails, SmartTags™, onsite billing, and access control, will no longer function.