If your address ends in your own domain, yes. The address belongs to the domain, which you own; the mailbox behind it is rented from the host, and a rented mailbox can be swapped for another one, or for nothing at all.
Everything below follows from one fact. An address like you@yourcompany.com is two things: a domain, yourcompany.com, which you pay a registrar for and which points wherever you tell it, and a mailbox, which a host runs for you and which stores the messages. Cancel the host and the mailbox goes. The domain, and so the address, stays yours, and you can point it at a new mailbox, at a forwarder, or at nothing.
If you only need the address kept alive and never need to send from it, free business email on your domain explains the free forwarding route in full. The rest of this page covers the questions that come up either way.
The exception is an address that is not on your domain: anything ending in gmail.com, outlook.com, or a host's own domain such as yourname@yourhost.net. Those addresses belong to the provider and end when the account does.
The order that avoids a gap
Do not cancel first. Cancellation at most hosts is immediate or takes effect at the end of the billing period, and the mailbox is usually deleted within days of that. So the sequence is: decide where the address will point next, set that up, move the mail, switch the DNS, and only then cancel.
Where it points next is one of three places. A new mailbox at another host, which is the usual answer and the one moving email without losing mail walks through step by step. A forwarder, which keeps the address alive for free by delivering anything sent to it into another inbox you already have. Or nothing, if the address is retired, in which case you still want a forwarder for a few months so that stragglers reach you.
The DNS switch is the moment the address changes hands. Your domain's MX records say which servers receive its mail; change them to the new host's or the forwarder's and new mail stops arriving at the old host within minutes. Everything already in the old mailbox stays there until you cancel, which is why the copy comes before the switch and the cancellation comes last.
The address is the domain. The mailbox is rented. Cancel last.
FAQs
What happens to my old mail when I cancel?
The host deletes the mailbox, usually within days of the cancellation taking effect, and the messages with it. Copy them out first over IMAP, or export them from the host's webmail, while the account is still open.
How long do I have after cancelling?
It varies by host, from immediate deletion to a grace period of a few weeks. Assume you have none, and finish the copy before you cancel rather than after.
Can I keep the address for free?
Yes, as a forwarder. Point the domain at a forwarding service and anything sent to you@yourcompany.com lands in another inbox. Faivelo's free plan is exactly this: unlimited forwarding aliases and a catch-all on your domain, with no mailbox. You cannot send as the address from a forwarder alone, so people who need to reply from it usually want a mailbox, which on Faivelo is $6 a month for the whole domain.
Will my contacts need a new address?
No. The address does not change. Only the servers behind it do, and your contacts never see those.
What breaks if I let the mailbox go without a plan?
Anything that sends you a code or a reset link: your bank, your registrar, app stores, payment processors, social accounts. If the address bounces when they write, recovering those accounts gets hard. A forwarder for a few months prevents this even for an address you are retiring.
I bought the domain from the same company as the email. Can I still leave?
Yes. Cancel the email product, not the domain. Keep the domain registered there, or transfer it elsewhere; either way, its DNS can point at any email host you choose.
Does cancelling web hosting cancel my email too?
At many web hosts, yes: mailboxes live inside the hosting account and disappear with it. Treat it the same way: copy, re-point the domain, then cancel.
Can I come back to the same address later?
Any time, as long as you keep the domain registered. Point its MX records at a new mailbox and the address works again.
Keep the address, swap the mailbox
Add your domain to Faivelo, copy the old mailbox over before you cancel, and let it write the new records at your registrar. Forwarding is free; a full mailbox is $6 a month for the whole domain.