That depends!
While we do host your website with all of its files, some hosting providers have other services that you might be using like:
– Email Hosting
– Domain Hosting
So if you cancel all of your old hosting provider services, you risk cancelling some critical elements of your web presence.
And while some of the providers will allow you to cancel your website hosting and still keep the other services, others will not.
To conclude, if you are sure that you don’t have any other services except website hosting with your old provider – it is safe to cancel! But, if you are not sure about this, the best move is to contact your hosting provider support and gain more info about the services they’re providing for you.