Paypal cancelation for members!

If a member cancel his membership vía paypal, I mean loginig into paypal and cancel the recurring payments, will the membership plugin notice this and automatizally cancel the accesse for that particular member?

I'm worried about this, because I know tat they could manage their memberships through the button and then being redirected to paypal, but if they just go directly, will the membership process this and close the access?

Thanyou in advance, please explain me this...