We have articles on what suspended bounces are. If a contact is bouncing as non-existent enough, from you or other customers of ours sending to them, there's not much that contact could really do - it's their network/IP that's providing the bounce code. They can try safelisting your email addresses, as just another layer of letting their email program / network know to trust email you're sending, regardless of source. If the contact is another business or organization with higher level network security, it may be worth having them reach out to their IT to make sure our domains are safelisted as well.
You can try unsuspending them individually within your account, or if you need a bunch of them unsuspended at once then our phone support can assist. However, if the contact bounces as non-existent again after sending a follow-up email to them (such a s a quicksend of the last email they should've received), then they'll be suspended in our system again.
It can help if you setup your account for self-authentication, as lacking this when you have your own domain can make some receiving networks treat the email more suspiciously (since the email is actually coming from a 3rd party source- us). Self-authentication essentially tells receiving networks that emails being sent through us by you should be treated as though they are coming directly from you. Doing this prior to sending to a bunch of contacts you've unsuspended may result in those previously "non-existent" addresses being fully open to receiving the emails.
If you're running into an issue where you're dealing with potentially dozens of what-should-be viable contacts being suspended, then I'd recommend reaching out to our Delivery team directly. They can better assist with mass-unsuspensions, and also look into why so many allegedly viable contacts are bouncing as non-existent enough to trigger suspension in the first place. The Delivery team can also provide additional insight on avoiding this, as well as what self-authentication method work work best for your needs.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ William A Community & Social Media Support