MX records say where mail for a domain should be delivered. If they are wrong, missing, or point somewhere that does not answer, mail bounces or vanishes.
Enter a domain to see its mail servers in priority order, the addresses they resolve to, the provider hosting them, and whether anything is misconfigured: an alias where a hostname is required, a private address, a host that does not resolve, or missing reverse DNS.
With no MX, senders fall back to the domain's address record and deliver to the web server. That is legal but rarely intended.
It must not. The standard requires a hostname with an address record. Some senders refuse delivery otherwise.
Hosted providers such as Google Workspace and Microsoft 365 run redundant networks behind one or a few names. If you run your own server, publish at least two at different priorities, on separate infrastructure.