> Should we expect them to do this given that doing so may kill their entire business?

Absolutely.

Don't forget that these customers may just file a chargeback through their bank. I did this with a service called Classpass which misleadingly kept you signed up without any notice. I and my partner both filed chargebacks and overturned 6 months of subscriptions.

That sort of thing can really harm a SaaS on a number of fronts and so IMHO they should ask the customer after one billing cycle and no activity.