Your own account is unaffected. Your Beauty Passport, your appointment history and your data belong to you and stay with you — a studio leaving does not take any of it with them.
Upcoming appointments with that studio are a different matter. A studio that leaves in an orderly way contacts its clients first; one that simply stops has left you with a booking nobody is going to honour. If a studio's page disappears and you had a future appointment, treat that appointment as at risk and contact them directly on whatever number or handle you have.
Money you paid ahead — a deposit, a package, a gift card — was paid to that business, not to us. It is a debt they owe you, and it is a matter between you and them. That is worth knowing before you buy a package: prepaying is lending money to a small business, and a small business can close.
Tell us as well. We cannot recover what a studio owes you, but a studio disappearing on paid-up clients is something we act on.